The spin angular momentum is an observable measurement of the system. Its three components in space meet the same commutation relationship as the orbital angular momentum.Each particle has its own spin.The spin angular momentum of particles follows the general law of angular momentum.
First of allElementary particlePut forward rotation and correspondingangular momentumThe concept was created by Ralph Kronig, George Uhlenbeck and Samuel Goudsmit in 1925.However, later in quantum mechanics, through theoretical and experimental verification, it was found that basic particles can be regarded as indivisible point particles, so the rotation of objects can not be directly applied to the spin angular momentum, so only spin can be regarded as an internal property, an angular momentum inherent in particles, and its value isquantizationIt cannot be changed (but the direction of spin angular momentum can be changed through operation).
A particle whose spin is a half integer is calledFermion, obeyFermi Dirac statistics；A particle whose spin is a nonnegative integer is calledBoson, obeyBose Einstein statistics。The spin of a composite particle is the vector sum of the relative orbital angular momentum between its internal components and the spin of each component, that is, the sum is calculated according to the angular momentum addition rule in quantum mechanics.Among the discovered particles, if the spin is an integer, the maximum spin is 4;If the spin is a half integer, the maximum spin is 3/2.[1]
Spin is a property of microscopic particles.A particle with spin 0 looks the same from all directions, just like a point.A particle with spin 1 looks the same when rotated 360 degrees.The particle with spin 2 rotates 180 degrees, and the particle with spin 1/2 must rotate 2 circles to be the same.A particle with a spin of 1/2 makes up everything in the universe, while a particle with a spin of 0, 1, and 2 generates forces between material bodies.Fermions with half integer spin obeyPauli exclusion principleBosons do not obey Pauli's principle.
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The discovery of spin first appeared inAlkali metal elementEmission spectrum of the subject.In 1924,Wolfgang PauliFirst, we introduce what he calls "two valued quantum degree of freedom", which is related to the electrons in the outermost shell.This allowed him to formalize the Pauli exclusion principle, that is, no two electrons can share the same quantum state at the same time.
High spin state
The physical explanation of Pauli's "degree of freedom" was initially unknown.Ralph Kronig, an assistant of Land é, proposed in early 1925 that it was produced by the rotation of electrons.When Pauli heard this idea, he severely criticized it. He pointed out that in order to generate enough angular momentum, the imaginary surface of the electron must move faster than the speed of light.This would violaterelativity。Due largely to Pauli's criticism, Kronig decided not to publish his ideas.In the autumn of that year, two young Dutch physicists came up with the same idea, George Uhlenbeck and Samuel Goudsmit.stayPaul EhrenfestAt the suggestion of, they published their results in a small space.It got a positive reaction, especially after Llewellyn Thomas eliminated the two contradictory coefficients between the experimental results and Uhlenbeck's and Goudsmit's (and Kronig's unpublished) calculations.This contradiction is because the tangential structure of the electron pointing must be included in the calculation and attached to its position;withMathematical languageFor example, we need aFibre plexusDescription.The tangential bundle effect is additive and relativistic (for example, it disappears when c approaches infinity);When the tangential space orientation is not considered, its value is only half, and the sign is opposite.So thisCompound effectThe difference coefficient with the later is 2 (Thomas preparation).
Although he initially opposed the idea, Pauli formalized the spin theory in 1927, using the modern quantum mechanics theory discovered by Elvin Schrodinger and Werner Heisenberg.He pioneered the use ofPauli matrixAs a group representation of spin operator, a binary spinor is introducedwave function。
Pauli's spin theory is nonrelativistic.However, in 1928,Paul Dirac PublishedDirac equationEquation, which describes the relativistic electron.In Dirac's equation, a quaternionSpinorThe so-called "Dirac spinor "Is used for the electronic wave function.In 1940, Pauli proved that "Spin statistical theorem", which indicates that fermions have half integer spins and bosons have integer spins.
Spin quantum number
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Elementary particle
For imagephoton, electrons, various quarks, etcElementary particle, both theoretical and experimental studies have found that their spin cannot be explained by the rotation of their smaller units around the center of mass (seeClassical electron radius）。Because these indivisible elementary particles can be considered as realPoint particleTherefore, spin, like mass and electricity, is the intrinsic property of elementary particles.[2]
Where ℏ=h/2 π isReduced Planck constant, s is called the spin quantum number, and the spin quantum number isintegerperhapsSemiinteger(0, 1/2, 1, 3/2, 2,……)。The spin quantum number can take a half integer value, which is the main difference between the spin quantum number and the orbital quantum number. The latter can only take an integer value.Spin quantum numberThe value of is only dependent on the type of particles, and cannot be changed by existing means (not confused with the direction of spin, see below).
For example, all electrons haves = 1/2The basic particles with 1/2 spin also includepositron、neutrinoAnd quarks, photons are particles with spin 1, which is theoretically assumedGravitonIt is a particle with spin 2, which has been foundHiggs bosonIt is special in elementary particles, whose spin is 0.
Subatomic particle
For imageproton、neutronandNucleusIn this waySubatomic particleSpin usually refers to the total angular momentum, that is, the sum of the spin angular momentum and the orbital angular momentum of subatomic particles.The spin of subatomic particles follows the same quantization conditions as other angular momentum.
spin
It is generally believed that the subatomic particle has a certain spin as the basic particle. For example, the proton is a particle with a spin of 1/2, which can be understood as a spin state of the subatomic particle with low energy. The spin state is determined by the structure of the internal spin angular momentum and orbital angular momentum of the subatomic particle.
It is difficult to derive the spin of subatomic particles from the first principle. For example, although we know that the proton is a particle with a spin of 1/2, the problem of the spin structure of the atomic nucleus is still an active research field.
Atoms and molecules
The spins of atoms and molecules are unpaired in atoms or moleculeselectron spinThe spin of unpaired electrons causes atoms and molecules to haveParamagnetism。
Spin and statistics
The spin of a particle is related to itsstatistical mechanicsThe properties in have profound influence, and particles with half integer spin followFermi Dirac statistics, calledFermion, they must occupy an antisymmetric quantum state (seeDistinguishable particle）This property requires that fermions cannot occupy the samequantum state, which is calledPauli exclusion principle。On the other hand, particles with integral spin followBose Einstein statistics, calledBosonThese particles can occupy symmetric quantum states, so they can occupy the same quantum state.The proof of this is calledSpin statistical theory, based on quantum mechanics and special relativity.In fact, the connection between spin and statistics is an important conclusion of special relativity.
Direction of spin
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Spin projection quantum numbers and spin multiplets
In classical mechanics, the angular momentum of a particle not only has size (depending on how fast the particle rotates), but also has direction (depending on the rotation axis of the particle).Spin in quantum mechanics also has directions, but it appears in a more subtle form.
In quantum mechanics, the measurement of angular momentum component in any direction can only take the following values:
Where s is the spin quantum number discussed in the previous chapter.It can be seen that for a given s,
You can take "2s+1" different values.For example, for a particle with a spin of 1/2, "sz"Only two different values can be taken,+1/2 or - 1/2. The corresponding quantum states are that the particle spin points to the+z or - z direction respectively. Generally, we call these two quantum states" spin up "and" spin down ".
For a given quantum state, a spin vector can be given
, its components are the mathematical expected values of spin components along each coordinate axis, that is
。This vector describes the "direction" of spin, which corresponds to the concept of spin axis in classical physics.This vector is not very useful in practical quantum mechanical calculations, because it cannot be measured directly and accurately: according toUncertainty principle，sx、syandszYou cannot have a fixed value at the same time.But for a large number of particles placed in the same quantum state, such as those obtained by using the Stern Grach instrument, the spin vector does have a well-defined experimental significance.
Spin and magnetic moment
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Particles with spin haveMagnetic dipole moment, just like the rotating charged object in classical electrodynamics.The magnetic moment can be observed by a variety of experimental means, such as the deflection of the inhomogeneous magnetic field in the Stern Grach experiment, or the measurement of the magnetic field generated by the particles themselves.[3]
The intrinsic magnetic moment of an elementary particle with electric quantity q, mass m and spin S
by
The dimensionless quantity g is called g-factor. When there is only orbital angular momentum, g=1.
Electrons are charged elementary particles with non-zero magnetic moment.The theory of quantum electrodynamics successfully predicted the g-factor of the electron. Its experimental measurement value is − 2.002 319 304 3622 (15). The two digits in the brackets are the measurement uncertainty, which is derived from the standard deviation. The integer part 2 is derived from the Dirac equation (the Dirac equation is the basic equation connecting the electron spin with its electromagnetic properties),The fractional part (0.002 319 304...) comes from the interaction between the electron and the surrounding electromagnetic field, including the electromagnetic field generated by the electron itself.
Spin and Chirality
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Leptons are spin ⁄twoA particle can only be in two spin states: spin up or spin down.Spin statistical theoremClassify them as fermions according to spin, and observePauli exclusion principleTherefore, any two identical leptons cannot occupy the same quantum state at the same time.
ChiralityAndHelicity(helicity) are two properties closely related to spin, and helicity is related to the relative direction between spin and momentum of particles;If it is in the same direction, the particles have right hand helicity; otherwise, the particles have left hand helicity.For particles without mass, the relative direction is independent of the reference system. However, for particles with massLorentz transformationTo change the reference system, the particle momentum is different from different reference systems, so the helicity can be changed from right-hand helicity to left-hand helicity, or from left-hand helicity to right-hand helicity.Chirality is achieved byPoincare group(Poincar é group).For particles without mass, chirality is consistent with helicity;For particles with mass, chirality is different from helicity.
In many quantum field theories, such as quantum electrodynamics and quantum chromodynamics, there is no distinction between left-handed and right-handed fermions. However, in the standard modelWeak interactionIn theory, left-handed and right-handed fermions distinguished according to chirality are treated asymmetrically, only left-handed fermions participate in weak interactions, and right-handed neutrinos do not exist.This isParity violationA typical example of.
From the book of quantum mechanics of independent scholars, "Seeing Little and Knowing Little"
Spintronics
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SwedenAccording to the Royal Academy of Sciences, in 2007NobelThe physics prize is awarded fromComputer hard diskThe technical root of reading data.French scientist Phil and German scientistPeter Grunberg Discovered in 1988Giant magnetoresistance effect, which greatly improves the performance of devices, making our computer hard disks smaller and smaller, but larger and larger.
Atomic spin
However, this discovery is not only so great.The reporter of the Science Times interviewed four scholars in this field.amongChinese Academy of SciencesZhu Tao, a researcher at the Institute of Physics, said: "Phil and Greenberger planted a seed. With the breakthrough in application in the 1990s, the seed grew into a young plant——SpintronicsThis is a fast growing and promising branch of magnetism. "
