"Harmonic oscillator in quantum mechanics"의 두 판 사이의 차이
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<h5>introduction</h5> | <h5>introduction</h5> | ||
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| + | <h5>harmonic oscillator in classical mechanics</h5> | ||
* 고전역학에서의 조화진동자 | * 고전역학에서의 조화진동자 | ||
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| + | <h5>creation and annhilation operators</h5> | ||
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| + | <h5>energy</h5> | ||
According to quantum mechanics, a harmonic oscillator that vibrates with frequency <math>\omega</math> can have energy <math>1/2\omega, (1 +1/2)\omega, (2 +1/2)\omega,(3 +1/2)\omega,\cdots</math> in units where Planck’s constant equals 1. | According to quantum mechanics, a harmonic oscillator that vibrates with frequency <math>\omega</math> can have energy <math>1/2\omega, (1 +1/2)\omega, (2 +1/2)\omega,(3 +1/2)\omega,\cdots</math> in units where Planck’s constant equals 1. | ||
The lowest energy is not zero! It’s <math>\omega/2</math>. This is called the ground state energy of the oscillator. | The lowest energy is not zero! It’s <math>\omega/2</math>. This is called the ground state energy of the oscillator. | ||
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| + | <h5>path integral formulation</h5> | ||
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| 37번째 줄: | 63번째 줄: | ||
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5> | ||
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* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
* http://www.scholarpedia.org/ | * http://www.scholarpedia.org/ | ||
2010년 9월 22일 (수) 17:55 판
introduction
harmonic oscillator in classical mechanics
- 고전역학에서의 조화진동자
- 고전역학에서의 가적분성 항목 참조
creation and annhilation operators
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.
path integral formulation
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