"Quantum scattering"의 두 판 사이의 차이
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6번째 줄: | 6번째 줄: | ||
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+ | <h5>harmonic</h5> | ||
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+ | * [[harmonic oscillator in quantum mechanics]] | ||
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<h5>example</h5> | <h5>example</h5> | ||
− | \[Lambda] := -1<br> u[x_] := -2 Sech[x]^2<br> f[x_] := Sech[x]<br> Simplify[D[D[f[x], x], x] + (\[Lambda] - u[x]) f[x]]<br> Plot[u[x], {x, -5, 5}] | + | # \[Lambda] := -1<br> u[x_] := -2 Sech[x]^2<br> f[x_] := Sech[x]<br> Simplify[D[D[f[x], x], x] + (\[Lambda] - u[x]) f[x]]<br> Plot[u[x], {x, -5, 5}] |
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2011년 2월 8일 (화) 04:10 판
introduction
- \(\varphi_{xx}+(\lambda-u)\varphi=0\)
- discrete spectrum \(\lambda<0\)
- continuous spectrum \(\lambda>0\)
harmonic
continuous spectrum
- \(a(k)e^{-ikx}+b(k)e^{ikx}\)
- a(k) transmission coefficient
- b(k) reflection coefficient
time independent Schrodinger equation
- Schrodinger equation
\(E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi\) - \(\varphi_{xx}+(\lambda-u)\varphi=0\)
example
- \[Lambda] := -1
u[x_] := -2 Sech[x]^2
f[x_] := Sech[x]
Simplify[D[D[f[x], x], x] + (\[Lambda] - u[x]) f[x]]
Plot[u[x], {x, -5, 5}]
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
articles
- http://en.wikipedia.org/wiki/Schrödinger_equation
- http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)
- 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