SPIN selling is a sales method developed by Neil Rackham and described in his book of the same name. The SPIN method has become one of the most widely used. Using this method you can achieve very high results in personal sales, Neil Rackham was able to prove this by conducting extensive research. And despite the fact that recently many have begun to believe that this sales method is becoming irrelevant, almost all large companies use the SPIN sales technique when training salespeople.
What is SPIN sales
In short, SPIN selling is a way of leading a client to a purchase by asking certain questions one by one; you are not presenting the product openly, but rather pushing the client to independently come to a decision to make a purchase. The SPIN method is best suited for so-called “long sales”, often these include sales of expensive or complex goods. That is, SPIN should be used when it is not easy for the client to make a choice. The need for this sales methodology arose primarily due to increased competition and market saturation. The client has become more discerning and experienced and this has required more flexibility from sellers.
The SPIN sales technique is divided into the following blocks of questions:
- WITH situational questions (Situation)
- P problematic issues (Problem)
- AND compelling questions (Implication)
- N guiding questions (Need-payoff)
It’s worth noting right away that SPIN sales are quite labor-intensive. The point is that in order to put this technique into practice, you need to know the product very well, have good experience in selling this product, such a sale itself takes a lot of time from the seller. Therefore, SPIN sales should not be used in the mass segment, for example in, because if the purchase price is low and the demand for the product is already high, then there is no point in spending a lot of time on long communication with the client, it is better to spend time on advertising and.
SPIN sales are based on the fact that the client, when directly offering a product by the seller, often includes a defense mechanism of denial. Buyers are pretty tired of being constantly being sold something and reacting negatively to the very fact of the offer. Although the product itself may be needed, it’s just that at the time of presentation the client thinks not that he needs the product, but that why is he being offered it? The use of the SPIN sales technique forces the client to make an independent purchasing decision, that is, the client does not even understand that his opinion is being controlled by asking the right questions.
SPIN sales technique
The SPIN sales technique is a sales model based not only on, but on theirs. In other words, to successfully use this sales technique, the seller must be able to ask the right questions. To begin with, let’s look at each group of SPIN sales technique questions separately:
Situational questions
This type of question is needed to fully identify his primary interests. The purpose of situational questions is to find out the client’s experience of using the product you are going to sell, his preferences, and for what purposes it will be used. As a rule, about 5 open questions and several clarifying questions are required. Based on the results of this block of questions, you should liberate the client and set him up for communication, which is why it is worth paying attention to open questions, as well as using. In addition, you must collect all the necessary information to pose problematic questions in order to effectively identify key needs worth using. As a rule, the block of situational questions takes the longest time. When you have received the necessary information from the client, you need to move on to problematic issues.
Problematic issues
By asking problematic questions, you must draw the client's attention to the problem. It is important at the stage of situational questions to understand what is important to the client. For example, if the client is always talking about money, then it would be logical to ask problematic questions regarding money: “Are you satisfied with the price you are paying now?”
If you haven't decided on your needs and don't know what problematic questions to ask. You need to have a number of prepared, standard questions that address various difficulties that the client may encounter. Your main goal is to identify the problem and the main thing is that it is important to the client. For example: a client may admit that he is overpaying for the services of the company he is using now, but he does not care about this, since the quality of services is important to him, not the price.
Probing Questions
This type of question is aimed at determining how important this problem is for him, and what will happen if it is not solved now. Extractive questions should make it clear to the client that by solving the current problem, he will benefit.
The difficulty with elicitation questions is that they cannot be thought through in advance, unlike the others. Of course, with experience, you will develop a pool of such questions, and you will learn to use them depending on the situation. But initially, many sellers who are mastering SPIN selling have difficulty asking such questions.
The essence of elicitation questions is to establish for the client the investigative connection between the problem and its solution. Once again, I would like to note that in SPIN sales, you cannot tell the client: “our product will solve your problem.” You must formulate the question so that in response the client himself says that he will be helped to solve the problem.
Guiding Questions
Guiding questions should help you; at this stage, the client should tell you for you all the benefits that he will receive from your product. Guiding questions can be compared to a positive way to close a transaction, only the seller does not summarize all the benefits that the client will receive, but vice versa.
So, let’s completely abstract ourselves and forget any classical definitions. Because with pin is a concept unique to the quantum world. Let's try to figure out what it is.
More useful information for students is in our telegram.
Spin and angular momentum
Spin(from English spin– rotate) – the intrinsic angular momentum of an elementary particle.
Now let's remember what angular momentum is in classical mechanics.
Momentum is a physical quantity that characterizes rotational motion, more precisely, the amount of rotational motion.
In classical mechanics, angular momentum is defined as the vector product of a particle’s momentum and its radius vector:
By analogy with classical mechanics spin characterizes the rotation of particles. They are represented in the form of tops rotating around an axis. If a particle has a charge, then, when rotating, it creates a magnetic moment and is a kind of magnet.
However, this rotation cannot be interpreted classically. All particles, in addition to spin, have an external or orbital angular momentum, which characterizes the rotation of the particle relative to some point. For example, when a particle moves along a circular path (an electron around a nucleus).
Spin is its own angular momentum , that is, characterizes the internal rotational state of the particle regardless of the external orbital angular momentum. Wherein spin does not depend on external movements of the particle .
It is impossible to imagine what is rotating inside the particle. However, the fact remains that for charged particles with oppositely directed spins, the trajectories of motion in a magnetic field will be different.
Spin quantum number
To characterize spin in quantum physics, it was introduced spin quantum number.
Spin quantum number is one of the quantum numbers inherent in particles. Often the spin quantum number is simply called spin. However, it should be understood that the spin of a particle (in the sense of its own angular momentum) and the spin quantum number are not the same thing. The spin number is denoted by the letter J and takes a number of discrete values, and the spin value itself is proportional to the reduced Planck constant:
Bosons and fermions
Different particles have different spin numbers. So, the main difference is that some have a whole spin, while others have a half-integer. Particles with integer spin are called bosons, and half-integer ones are called fermions.
Bosons obey Bose-Einstein statistics, and fermions obey Fermi-Dirac statistics. In an ensemble of particles consisting of bosons, any number of them can be in the same state. With fermions, the opposite is true - the presence of two identical fermions in one system of particles is impossible.
Bosons: photon, gluon, Higgs boson. - in a separate article.
Fermions: electron, lepton, quark
Let's try to imagine how particles with different spin numbers differ using examples from the macrocosm. If the spin of an object is zero, then it can be represented as a point. From all sides, no matter how you rotate this object, it will be the same. With a spin of 1, rotating the object 360 degrees returns it to a state identical to its original state.
For example, a pencil sharpened on one side. A spin of 2 can be imagined as a pencil sharpened on both sides - when we rotate such a pencil 180 degrees, we will not notice any changes. But a half-integer spin equal to 1/2 is represented by an object, to return which to its original state you need to make a revolution of 720 degrees. An example would be a point moving along a Mobius strip.
So, spin- a quantum characteristic of elementary particles, which serves to describe their internal rotation, the angular momentum of a particle, independent of its external movements.
We hope that you will master this theory quickly and be able to apply the knowledge in practice if necessary. Well, if a quantum mechanics problem turns out to be too difficult or you can’t do it, don’t forget about the student service, whose specialists are ready to come to the rescue. Considering that Richard Feynman himself said that “no one fully understands quantum physics,” it is quite natural to turn to experienced specialists for help!
L3 -12
Electron spin. Spin quantum number. During classical orbital motion, an electron has a magnetic moment. Moreover, the classical ratio of the magnetic moment to the mechanical moment matters
, (1) where 
And 
– magnetic and mechanical moment, respectively. Quantum mechanics leads to a similar result. Since the projection of the orbital moment to a certain direction can only take discrete values, the same applies to the magnetic moment. Therefore, the projection of the magnetic moment onto the direction of the vector B
for a given value of the orbital quantum number l can take values
Where 
- so-called Bohr magneton.
O. Stern and W. Gerlach carried out direct measurements of magnetic moments in their experiments. They discovered that a narrow beam of hydrogen atoms, known to be in s-state, in a non-uniform magnetic field it splits into two beams. In this state, the angular momentum, and with it the magnetic moment of the electron, is zero. Thus, the magnetic field should not affect the movement of hydrogen atoms, i.e. there should be no splitting.
To explain this and other phenomena, Goudsmit and Uhlenbeck put forward the assumption that the electron has its own angular momentum 
, not related to the movement of the electron in space. This own moment was called spin.
It was initially assumed that spin was due to the rotation of the electron around its axis. According to these ideas, relation (1) must be satisfied for the ratio of magnetic and mechanical moments. It was experimentally established that this ratio is actually twice as large as for orbital moments
. For this reason, the idea of an electron as a rotating ball turns out to be untenable. In quantum mechanics, the spin of an electron (and all other microparticles) is considered as an internal inherent property of the electron, similar to its charge and mass.
The magnitude of the intrinsic angular momentum of a microparticle is determined in quantum mechanics using spin quantum numbers(for electron 
)
. The projection of a spin onto a given direction can take on quantized values that differ from each other by 
. For an electron
Where 
–magnetic spin quantum number.
To fully describe the electron in an atom, it is therefore necessary to specify, along with the main, orbital and magnetic quantum numbers, the magnetic spin quantum number.
Identity of particles. In classical mechanics, identical particles (say, electrons), despite the identity of their physical properties, can be marked by numbering, and in this sense the particles can be considered distinguishable. In quantum mechanics the situation changes radically. The concept of a trajectory loses its meaning, and, consequently, as the particles move, they become entangled. This means that it is impossible to tell which of the initially labeled electrons ended up at which point.
Thus, in quantum mechanics, identical particles completely lose their individuality and become indistinguishable. This is a statement or, as they say, principle of indistinguishability identical particles has important consequences.
Consider a system consisting of two identical particles. Due to their identity, the states of the system obtained from each other by rearranging both particles must be physically completely equivalent. In the language of quantum mechanics this means that
Where 
,
– sets of spatial and spin coordinates of the first and second particles. As a result, two cases are possible
Thus, the wave function is either symmetric (does not change when the particles are rearranged) or antisymmetric (i.e., changes sign when rearranged). Both of these cases occur in nature.
Relativistic quantum mechanics establishes that the symmetry or antisymmetry of wave functions is determined by the spin of particles. Particles with half-integer spin (electrons, protons, neutrons) are described by antisymmetric wave functions. Such particles are called fermions, and are said to obey Fermi-Dirac statistics. Particles with zero or integer spin (such as photons) are described by symmetric wave functions. These particles are called bosons, and are said to obey Bose-Einstein statistics. Complex particles (for example, atomic nuclei) consisting of an odd number of fermions are fermions (the total spin is half-integer), and those consisting of an even number are bosons (the total spin is integer).
Pauli's principle. Atomic shells. If identical particles have the same quantum numbers, then their wave function is symmetric with respect to the permutation of particles. It follows that two fermions included in this system cannot be in the same states, since for fermions the wave function must be antisymmetric.
From this position it follows Pauli's exclusion principle: Any two fermions cannot be in the same state at the same time.
The state of an electron in an atom is determined by a set of four quantum numbers:
main n(
,
orbital l(
),
magnetic 
(
),
magnetic spin 
(
).
The distribution of electrons in an atom according to states obeys the Pauli principle, therefore two electrons located in an atom differ in the values of at least one quantum number.
A certain value n corresponds 
various states that differ l And 
. Because 
can take only two values ( 
), then the maximum number of electrons in states with a given n, will be equal 
. The collection of electrons in a multielectron atom that have the same quantum number n, called electron shell. In each electrons are distributed according to subshells, corresponding to this l. Maximum number of electrons in a subshell with a given l equals 
. Shell designations, as well as the distribution of electrons across shells and subshells are presented in the table.
Mendeleev's periodic table of elements. The Pauli principle can be used to explain the Periodic Table of Elements. The chemical and some physical properties of elements are determined by their outer valence electrons. Therefore, the periodicity of the properties of chemical elements is directly related to the nature of filling the electron shells in the atom.
The elements in the table differ from each other in the charge of the nucleus and the number of electrons. When moving to a neighboring element, the latter increase by one. Electrons fill the levels so that the energy of the atom is minimal.
In a multielectron atom, each individual electron moves in a field that differs from the Coulomb field. This leads to the fact that the degeneracy in orbital momentum is removed 
. Moreover, with an increase l energy levels with the same n increases. When the number of electrons is small, the difference in energy with different l and identical n not as great as between states with different n. Therefore, electrons first fill shells with smaller n, beginning with s subshells, successively moving to larger values l.
The only electron of the hydrogen atom is in state 1 s. Both electrons of the He atom are in state 1 s with antiparallel spin orientations. The filling ends at the helium atom K-shells, which corresponds to the end of period I of the periodic table.
The third electron of the Li atom( Z3)occupies the lowest free energy state with n2 ( L-shell), i.e. 2 s-state. Since it is bound weaker than other electrons to the nucleus of the atom, it determines the optical and chemical properties of the atom. The process of filling electrons in the second period is not disrupted. The period ends with neon, which L- the shell is completely filled.
In the third period, filling begins M-shells. The eleventh electron of the first element of a given period Na( Z11) occupies the lowest free state 3 s. 3s-electron is the only valence electron. In this regard, the optical and chemical properties of sodium are similar to those of lithium. The elements following sodium have their subshells filled normally 3 s and 3 p.
For the first time, a violation of the usual sequence of filling levels occurs at K( Z19). Its nineteenth electron would have to occupy 3 d-state in the M-shell. For this general configuration, subshell 4 s turns out to be energetically lower than subshell 3 d. In this connection, when the entire filling of the shell M is incomplete, the filling of the shell N begins. In optical and chemical terms, the K atom is similar to the Li and Na atoms. All these elements have a valence electron in s-condition.
With similar deviations from the usual sequence, repeated from time to time, the electronic levels of all atoms are built. In this case, similar configurations of outer (valence) electrons are periodically repeated (for example, 1 s, 2s, 3s etc.), which determines the repeatability of the chemical and optical properties of atoms.
X-ray spectra. The most common source of X-ray radiation is an X-ray tube, in which electrons highly accelerated by an electric field bombard the anode. When electrons decelerate, X-rays are produced. The spectral composition of X-ray radiation is a superposition of a continuous spectrum limited on the short wavelength side by a boundary length 
, and line spectrum - a collection of individual lines against the background of a continuous spectrum.
The continuous spectrum is due to the emission of electrons during their deceleration. That's why they call him bremsstrahlung radiation. The maximum energy of a bremsstrahlung quantum corresponds to the case when the entire kinetic energy of the electron is converted into the energy of an X-ray photon, i.e.
, Where U– accelerating potential difference of the X-ray tube. Hence the cutoff wavelength. (2) By measuring the short-wave limit of bremsstrahlung, one can determine Planck's constant. Of all the methods for determining 
This method is considered the most accurate.
At a sufficiently high electron energy, individual sharp lines appear against the background of a continuous spectrum. The line spectrum is determined only by the anode material, so this radiation is called characteristic radiation.
The characteristic spectra are noticeably simple. They consist of several series, designated by letters K,L,M, N And O. Each series contains a small number of lines, designated in order of increasing frequency by the indices , , ... ( 
,
,
,
…;
,
,
, … etc.). The spectra of different elements have a similar character. As the atomic number increases Z the entire X-ray spectrum is entirely shifted to the short-wavelength region without changing its structure (Fig.). This is explained by the fact that X-ray spectra arise from transitions of internal electrons, which are similar for different atoms.
The diagram for the appearance of X-ray spectra is shown in Fig. Excitation of an atom consists of the removal of one of the internal electrons. If one of the two electrons escapes K-layer, then the vacated space can be occupied by an electron from some outer layer ( L,M,N etc.). In this case, there arises K-series. Other series arise similarly, observed, however, only for heavy elements. Series K necessarily accompanied by the rest of the series, since when its lines are emitted, the levels in the layers are released L,M etc., which will in turn be filled with electrons from higher layers.
While studying the X-ray spectra of elements, G. Moseley established a relationship called Moseley's law
, (3) where is the frequency of the characteristic X-ray radiation line, R– Rydberg constant, 
(defines x-ray series), 
(defines the line of the corresponding series), – shielding constant.
Moseley's law allows one to accurately determine the atomic number of a given element from the measured wavelength of X-ray lines; this law played a large role in the placement of elements in the periodic table.
Moseley's Law can be given a simple explanation. Lines with frequencies (3) arise during the transition of an electron located in the charge field 
, from level with number n to the level with number m. The shielding constant arises from the shielding of the kernel Ze other electrons. Its meaning depends on the line. For example, for 
-lines 
and Moseley's law will be written in the form
.
Communication in molecules. Molecular spectra. There are two types of bonds between atoms in a molecule: ionic and covalent bonds.
Ionic bond. If two neutral atoms are gradually brought closer to each other, then in the case of an ionic bond there comes a moment when the outer electron of one of the atoms prefers to join the other atom. An atom that has lost an electron behaves like a particle with a positive charge e, and an atom that has acquired an extra electron is like a particle with a negative charge e. An example of a molecule with an ionic bond is HCl, LiF, etc.
Covalent bond. Another common type of molecular bond is a covalent bond (for example, in H 2 , O 2 , CO molecules). The formation of a covalent bond involves two valence electrons of neighboring atoms with oppositely directed spins. As a result of the specific quantum movement of electrons between atoms, an electron cloud is formed, which causes the attraction of atoms.
Molecular spectra more complex than atomic spectra, since in addition to the movement of electrons relative to nuclei in the molecule, oscillatory movement of nuclei (together with the internal electrons surrounding them) around equilibrium positions and rotational molecular movements.
Molecular spectra arise from quantum transitions between energy levels 
And 
molecules according to the ratio
, Where 
– energy of an emitted or absorbed frequency quantum. With Raman scattering of light 
is equal to the difference between the energies of the incident and scattered photons.
Electronic, vibrational and rotational movements of molecules correspond to energy 
,
And 
. Total energy of a molecule E can be represented as the sum of these energies
, and in order of magnitude, where m– electron mass, M– molecular mass ( 
). Hence 
. Energy 
eV, 
eV, 
eV.
According to the laws of quantum mechanics, these energies take only quantized values. The diagram of the energy levels of a diatomic molecule is shown in Fig. (for example, only two electronic levels are considered - shown in thick lines). Electronic energy levels are far apart from each other. The vibrational levels are located much closer to each other, and the rotational energy levels are located even closer to each other.
Typical molecular spectra are striped, in the form of a collection of bands of varying widths in the UV, visible and IR regions of the spectrum.
In this regard, they speak of a whole or half-integer spin of a particle.
The existence of spin in a system of identical interacting particles is the cause of a new quantum mechanical phenomenon that has no analogy in classical mechanics, exchange interaction.
The spin vector is the only quantity that characterizes the orientation of a particle in quantum mechanics. From this position it follows that: at zero spin, a particle cannot have any vector or tensor characteristics; vector properties of particles can only be described by axial vectors; particles can have magnetic dipole moments and cannot have electric dipole moments; particles can have an electric quadrupole moment and cannot have a magnetic quadrupole moment; A nonzero quadrupole moment is possible only for particles with a spin not less than unity.
The spin momentum of an electron or other elementary particle, uniquely separated from the orbital momentum, can never be determined through experiments to which the classical concept of particle trajectory is applicable.
The number of components of the wave function that describes an elementary particle in quantum mechanics increases with the spin of the elementary particle. Elementary particles with spin are described by a one-component wave function (scalar), with spin 1 2 (\displaystyle (\frac (1)(2))) are described by a two-component wave function (spinor), with spin 1 (\displaystyle 1) are described by a four-component wave function (vector), with spin 2 (\displaystyle 2) are described by a six-component wave function (tensor).
What is spin - with examples
Although the term “spin” refers only to the quantum properties of particles, the properties of some cyclically acting macroscopic systems can also be described by a certain number that shows how many parts the rotation cycle of a certain element of the system must be divided into for it to return to a state indistinguishable from the initial one.
It's easy to imagine spin equal to 0: this is the point - she looks the same from all sides, no matter how you slice it.
Example spin equal to 1, most ordinary objects can serve without any symmetry: if such an object is rotated 360 degrees, then this item will return to its original state. For example, you can put a pen on the table, and after turning it 360°, the pen will again lie the same way as before the rotation.
As an example spin equal to 2 you can take any object with one axis of central symmetry: if you rotate it 180 degrees, it will be indistinguishable from the original position, and in one full rotation it becomes indistinguishable from the original position 2 times. An example from life would be an ordinary pencil, only sharpened on both sides or not sharpened at all - the main thing is that it is without inscriptions and monochromatic - and then after turning 180° it will return to a position indistinguishable from the original one. Hawking used an ordinary playing card such as a king or queen as an example.
But with half a whole spin equal 1 / 2 a little more complicated: it turns out that the system returns to its original position after 2 full revolutions, that is, after a rotation of 720 degrees. Examples:
- If you take a Möbius strip and imagine that an ant is crawling along it, then, having made one turn (traversing 360 degrees), the ant will end up at the same point, but on the other side of the sheet, and to return to the point where it started, it will have to go all the way 720 degrees.
- four-stroke internal combustion engine. When the crankshaft is rotated 360 degrees, the piston will return to its original position (for example, top dead center), but the camshaft rotates 2 times slower and will make a full revolution when the crankshaft is rotated 720 degrees. That is, when the crankshaft is turned 2 revolutions, the internal combustion engine will return to the same state. In this case, the third measurement will be the position of the camshaft.
Examples like these can illustrate the addition of spins:
- Two identical pencils sharpened only on one side (the “spin” of each is 1), fastened with their sides so that the sharp end of one is next to the blunt end of the other (↓). Such a system will return to an indistinguishable state from the initial state when rotated only 180 degrees, that is, the “spin” of the system becomes equal to two.
- Multi-cylinder four-stroke internal combustion engine (“spin” of each cylinder is equal to 1/2). If all cylinders operate in the same way, then the conditions in which the piston is at the beginning of the power stroke in any of the cylinders will be indistinguishable. Consequently, a two-cylinder engine will return to a state indistinguishable from the original one every 360 degrees (total "spin" - 1), a four-cylinder engine - after 180 degrees ("spin" - 2), an eight-cylinder engine - after 90 degrees ("spin" - 4 ).
Spin properties
Any particle can have two types of angular momentum: orbital angular momentum and spin.
Unlike orbital angular momentum, which is generated by the motion of a particle in space, spin is not associated with motion in space. Spin is an internal, exclusively quantum characteristic that cannot be explained within the framework of relativistic mechanics. If we imagine a particle (for example, an electron) as a rotating ball, and spin as the torque associated with this rotation, then it turns out that the transverse velocity of the particle shell must be higher than the speed of light, which is unacceptable from the position of relativism.
Being one of the manifestations of angular momentum, spin in quantum mechanics is described by the vector spin operator s → ^ , (\displaystyle (\hat (\vec (s))),) the algebra of whose components completely coincides with the algebra of orbital angular momentum operators ℓ → ^ . (\displaystyle (\hat (\vec (\ell ))).) However, unlike orbital angular momentum, the spin operator is not expressed in terms of classical variables, in other words, it is only a quantum quantity. A consequence of this is the fact that spin (and its projections onto any axis) can take not only integer, but also half-integer values (in units of the Dirac constant ħ ).
Spin experiences quantum fluctuations. As a result of quantum fluctuations, only one spin component can have a strictly defined value, for example. In this case, the components J x , J y (\displaystyle J_(x),J_(y)) fluctuate around the average value. Maximum possible component value J z (\displaystyle J_(z)) equals J (\displaystyle J). At the same time the square J 2 (\displaystyle J^(2)) the total spin vector is equal to J (J + 1) (\displaystyle J(J+1)). Thus J x 2 + J y 2 = J 2 − J z 2 ⩾ J (\displaystyle J_(x)^(2)+J_(y)^(2)=J^(2)-J_(z)^(2 )\geqslant J). At J = 1 2 (\displaystyle J=(\frac (1)(2))) the root mean square values of all components due to fluctuations are equal J x 2 ^ = J y 2 ^ = J z 2 ^ = 1 4 (\displaystyle (\widehat (J_(x)^(2)))=(\widehat (J_(y)^(2)))= (\widehat (J_(z)^(2)))=(\frac (1)(4))).
The spin vector changes its direction during the Lorentz transformation. The axis of this rotation is perpendicular to the momentum of the particle and the relative velocity of the reference systems.
Examples
The spins of some microparticles are shown below.
| spin | common name for particles | examples |
|---|---|---|
| 0 | scalar particles | π mesons, K mesons, Higgs boson, 4 He atoms and nuclei, even-even nuclei, parapositronium |
| 1/2 | spinor particles | electron, quarks, muon, tau lepton, neutrino, proton, neutron, 3 He atoms and nuclei |
| 1 | vector particles | photon, gluon, W and Z bosons, vector mesons, orthopositronium |
| 3/2 | spin vector particles | Ω-hyperon, Δ-resonances |
| 2 | tensor particles | graviton, tensor mesons |
As of July 2004, the baryon resonance Δ(2950) with a spin of 15/2 has the maximum spin among the known baryons. The spin of stable nuclei cannot exceed 9 2 ℏ (\displaystyle (\frac (9)(2))\hbar ) .
Story
The term “spin” itself was introduced into science by S. Goudsmit and D. Uhlenbeck in 1925.
Mathematically, the theory of spin turned out to be very transparent, and later, by analogy with it, the theory of isospin was constructed.
Spin and magnetic moment
Despite the fact that spin is not associated with the actual rotation of the particle, it nevertheless generates a certain magnetic moment, which means it leads to additional (compared to classical electrodynamics) interaction with the magnetic field. The ratio of the magnitude of the magnetic moment to the magnitude of the spin is called the gyromagnetic ratio, and, unlike orbital angular momentum, it is not equal to the magneton ( μ 0 (\displaystyle \mu _(0))):
μ → ^ = g ⋅ μ 0 s → ^ . (\displaystyle (\hat (\vec (\mu )))=g\cdot \mu _(0)(\hat (\vec (s))).)The multiplier introduced here g called g-particle factor; the meaning of this g-factors for various elementary particles are actively studied in particle physics.
Spin and statistics
Due to the fact that all elementary particles of the same type are identical, the wave function of a system of several identical particles must be either symmetric (that is, does not change) or antisymmetric (multiplied by −1) with respect to the interchange of any two particles. In the first case, the particles are said to obey Bose–Einstein statistics and are called bosons. In the second case, the particles are described by Fermi-Dirac statistics and are called fermions.
It turns out that it is the value of the particle's spin that tells us what these symmetry properties will be. The spin-statistics theorem formulated by Wolfgang Pauli in 1940 states that particles with integer spin ( s= 0, 1, 2, …) are bosons, and particles with half-integer spin ( s= 1/2, 3/2, …) - fermions.
Generalization of spin
The introduction of spin was a successful application of a new physical idea: the postulation that there is a space of states that are in no way related to the movement of a particle in the ordinary
Contrary to popular belief, spin is a purely quantum phenomenon. Moreover, spin has nothing to do with the “rotation of a particle” around itself.
To understand correctly what spin is, let's first understand what a particle is. From quantum field theory we know that particles are those of a certain type of excitation of the primary state (vacuum) that have certain properties. In particular, some of these excitations have mass that reminds us very much of the traditional mass from Newton's laws. Some of these excitations have a non-zero charge, which is very similar to the charge from Coulomb's laws.
In addition to the properties that have their analogues in classical physics (mass, charge), it turns out (in experiments) that these excitations must have one more property that has absolutely no analogues in classical physics. I will emphasize this again: NO analogues (this is NOT particle rotation). During the calculations, it turned out that this spin is not a scalar characteristic of the particle, like mass or charge, but another (not vector).
It turns out that spin is an internal characteristic of such excitation, which in its mathematical properties (transformation law, for example) is very similar to the quantum moment.
Then it went on and on. It turned out that the properties of such excitations, their wave functions, very much depend on the magnitude of this very spin. Thus, a particle with spin 0 (for example, the Higgs boson) can be described by a one-component wave function, and for a particle with spin 1/2 there must be a two-component function (vector function) corresponding to the projection of the spin onto a given 1/2 or -1/2 axis. It also turned out that spin carries with it a fundamental difference between particles. Thus, for particles with an integer spin (0, 1, 2), the Bose-Einstein distribution law holds, which allows as many particles as desired to be in one quantum state. And for particles with half-integer spin (1/2, 3/2), due to the Pauli exclusion principle, the Fermi-Dirac distribution operates, which prohibits two particles from being in the same quantum state. Thanks to the latter, atoms have Bohr levels, because of this, connections are possible and, therefore, life is possible.
This means that spin specifies the characteristics of a particle and how it behaves when interacting with other particles. A photon has a spin equal to 1 and many photons can be very close to each other and not interact with each other, or photons with gluons, since the latter also have spin = 1, and so on. And electrons with a spin of 1/2 will repel each other (as they teach in school - from -, + from +.) Did I understand correctly?
And another question: what gives the particle itself the spin or why does the spin exist? If spin describes the behavior of particles, then what does the spin itself describe and make possible (any bosons (including those existing hypothetically) or so-called strings)?