"Klein-Gordon equation"의 두 판 사이의 차이
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| 5번째 줄: | 5번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* in condensed matter physics it describes long wavelength optical phonons | * in condensed matter physics it describes long wavelength optical phonons | ||
| 22번째 줄: | 22번째 줄: | ||
| − | ==Lorentz invariant commutation relation | + | ==Lorentz invariant commutation relation== |
| 30번째 줄: | 30번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[special and general relativity]] | * [[special and general relativity]] | ||
* [[sine-Gordon equation]] | * [[sine-Gordon equation]] | ||
2012년 10월 28일 (일) 14:30 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