"Harmonic oscillator in quantum mechanics"의 두 판 사이의 차이
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| 21번째 줄: | 21번째 줄: | ||
<h5>creation and annhilation operators</h5> | <h5>creation and annhilation operators</h5> | ||
| − | + | <math>a =\sqrt{m\omega \over 2\hbar} \left(x + {i \over m \omega} p \right)</math> | |
| + | |||
| + | <math>a^{\dagger} =\sqrt{m \omega \over 2\hbar} \left( x - {i \over m \omega} p \right)</math> | ||
| + | |||
| + | <math>H = \hbar \omega \left(a^{\dagger}a + 1/2\right)</math> | ||
| + | |||
| + | <math>\left[a , a^{\dagger} \right] = 1</math> | ||
| 37번째 줄: | 43번째 줄: | ||
| − | <h5> | + | <h5>Schrodinger equation</h5> |
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| + | * | ||
2010년 9월 22일 (수) 17:07 판
introduction
harmonic oscillator in classical mechanics
- 고전역학에서의 조화진동자
- 고전역학에서의 가적분성 항목 참조
creation and annhilation operators
\(a =\sqrt{m\omega \over 2\hbar} \left(x + {i \over m \omega} p \right)\)
\(a^{\dagger} =\sqrt{m \omega \over 2\hbar} \left( x - {i \over m \omega} p \right)\)
\(H = \hbar \omega \left(a^{\dagger}a + 1/2\right)\)
\(\left[a , a^{\dagger} \right] = 1\)
energy
According to quantum mechanics, a harmonic oscillator that vibrates with frequency \(\omega\) can have energy \(1/2\omega, (1 +1/2)\omega, (2 +1/2)\omega,(3 +1/2)\omega,\cdots\) in units where Planck’s constant equals 1.
The lowest energy is not zero! It’s \(\omega/2\). This is called the ground state energy of the oscillator.
Schrodinger equation
path integral formulation
history
encyclopedia
- http://ko.wikipedia.org/wiki/양자조화진동자
- http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
- 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