"Klein-Gordon equation"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | * | + | * free massive scalar field which describes the spin-0 particles |
| − | |||
* in condensed matter physics it describes long wavelength optical phonons | * in condensed matter physics it describes long wavelength optical phonons | ||
* formulated as a relativistic generalization of Schrodinger equation | * formulated as a relativistic generalization of Schrodinger equation | ||
| 24번째 줄: | 23번째 줄: | ||
<h5>plane wave solutions</h5> | <h5>plane wave solutions</h5> | ||
| − | * | + | * <math>u(x,t)=Ae^{i(kx-\omega t)}</math> or |
2010년 11월 9일 (화) 05:49 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
- \(u(x,t)=Ae^{i(kx-\omega t)}\) or
Lorentz invariant commutation relation
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
expositions
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field