"Klein-Gordon equation"의 두 판 사이의 차이
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<h5>plane wave solutions</h5> | <h5>plane wave solutions</h5> | ||
| − | * <math>u(x,t)=Ae^{i(kx-\omega t)}</math> | + | * <math>u(x,t)=Ae^{i(kx-\omega t)}</math> |
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<h5>Lorentz invariant commutation relation</h5> | <h5>Lorentz invariant commutation relation</h5> | ||
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* [[sine-Gordon equation]] | * [[sine-Gordon equation]] | ||
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2012년 2월 22일 (수) 11:16 판
introduction
- free massive scalar field which describes the spin-0 particles
- in condensed matter physics it describes long wavelength optical phonons
- formulated as a relativistic generalization of Schrodinger equation
- 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. \((\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0\)
- people found 2 problems of KG equations
- negative energy states
- negative probability density
- 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.
plane wave solutions
- \(u(x,t)=Ae^{i(kx-\omega t)}\)
Lorentz invariant commutation relation
history