"Spin system and Pauli exclusion principle"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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==introduction== | ==introduction== | ||
| + | * {{수학노트|url=스핀과 파울리의 배타원리}} | ||
| + | * the simplest example of quantum mechanical system | ||
| + | * quantization of the angular momentum | ||
| + | * measures as being some multiple of Planck's constant divided by $2\pi$ | ||
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==evolution of Pauli exclusion principle== | ==evolution of Pauli exclusion principle== | ||
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* originated from atomic spectroscopy | * originated from atomic spectroscopy | ||
* Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles | * Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles | ||
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* anti-commutation relations for particle creation and annihilation operators in quantum field theory | * anti-commutation relations for particle creation and annihilation operators in quantum field theory | ||
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==representation theory== | ==representation theory== | ||
| + | * concept from the representation of <math>SU(2)</math> | ||
| + | * half of highest weight is called the spin of the module | ||
| + | ** Casimir operator can also detect this number. | ||
| + | * spin <math>1/2</math> is the most important case since they are the matter particles | ||
| + | * this is why we have half-integral spin although those representation are integral highest weight representations. | ||
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==spin particle statstics== | ==spin particle statstics== | ||
| − | + | * Bosons | |
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** photon | ** photon | ||
** vector boson | ** vector boson | ||
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** follows Bose-Einstein statistics | ** follows Bose-Einstein statistics | ||
** force-transmitting particles | ** force-transmitting particles | ||
| − | * | + | * Fermions = spin- <math>1/2</math> particles |
| − | ** | + | ** quarks and leptons |
| − | ** | + | ** follows Fermi-Dirac statistics |
| − | ** | + | ** matter particles |
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==Dirac wave equation== | ==Dirac wave equation== | ||
| − | * [[Dirac equation]] | + | * [[Dirac equation]] |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 12월 15일 (일) 19:32 판
introduction
- 틀:수학노트
- the simplest example of quantum mechanical system
- quantization of the angular momentum
- measures as being some multiple of Planck's constant divided by $2\pi$
evolution of Pauli exclusion principle
- originated from atomic spectroscopy
- Dirac-antisymmetrizing the wave function for an assembly of indistinguishable particles
- Pauli's spin matrices
- anti-commutation relations for particle creation and annihilation operators in quantum field theory
representation theory
- concept from the representation of \(SU(2)\)
- half of highest weight is called the spin of the module
- Casimir operator can also detect this number.
- spin \(1/2\) is the most important case since they are the matter particles
- this is why we have half-integral spin although those representation are integral highest weight representations.
spin particle statstics
- Bosons
- photon
- vector boson
- Gluon
- follows Bose-Einstein statistics
- force-transmitting particles
- Fermions = spin- \(1/2\) particles
- quarks and leptons
- follows Fermi-Dirac statistics
- matter particles