"Klein-Gordon equation"의 두 판 사이의 차이
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| + | * [http://pythagoras0.springnote.com/pages/10686554 클라인-고든 방정식] | ||
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<h5>introduction</h5> | <h5>introduction</h5> | ||
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* in condensed matter physics it describes long wavelength optical phonons | * in condensed matter physics it describes long wavelength optical phonons | ||
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* there are real KG equation and complex KG equation<br> | * there are real KG equation and complex KG equation<br> | ||
** real case describes electrically neutral particles | ** real case describes electrically neutral particles | ||
** complex case describes charged particles | ** complex case describes charged particles | ||
* <math>(\Box + m^2) \psi = 0</math> i.e. <math>(\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0</math> | * <math>(\Box + m^2) \psi = 0</math> i.e. <math>(\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0</math> | ||
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* correct interpretations of <math>\phi</math> requires the idea of quantum field rather than the particle wavefunction<br> | * correct interpretations of <math>\phi</math> requires the idea of quantum field rather than the particle wavefunction<br> | ||
** negative probability density -> charge density | ** negative probability density -> charge density | ||
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** for example, <math>\pi</math>-meson | ** for example, <math>\pi</math>-meson | ||
* Thus the Dirac equation comes in to deal with spin-<math>1/2</math> particles. | * Thus the Dirac equation comes in to deal with spin-<math>1/2</math> particles. | ||
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2012년 8월 22일 (수) 05:35 판
introduction
- in condensed matter physics it describes long wavelength optical phonons
- there are real KG equation and complex KG equation
- real case describes electrically neutral particles
- complex case describes charged particles
- \((\Box + m^2) \psi = 0\) i.e. \((\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0\)
- correct interpretations of \(\phi\) requires the idea of quantum field rather than the particle wavefunction
- negative probability density -> charge density
- Dirac suggested Dirac sea by invoking the exclusion principle and then KG equation only applicable to spinless particles
- for example, \(\pi\)-meson
- Thus the Dirac equation comes in to deal with spin-\(1/2\) particles.
Lorentz invariant commutation relation