"Quantum scattering"의 두 판 사이의 차이
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| 4번째 줄: | 4번째 줄: | ||
* discrete spectrum <math>\lambda<0</math> | * discrete spectrum <math>\lambda<0</math> | ||
* continuous spectrum <math>\lambda>0</math> | * continuous spectrum <math>\lambda>0</math> | ||
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| + | <h5>continuous spectrum</h5> | ||
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| + | * <math>a(k)e^{-ikx}+b(k)e^{ikx}</math> | ||
| + | * a(k) transmission coefficient | ||
| + | * b(k) reflection coefficient | ||
| 13번째 줄: | 23번째 줄: | ||
* [[Schrodinger equation]]<br><math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math><br> | * [[Schrodinger equation]]<br><math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math><br> | ||
* <math>\varphi_{xx}+(\lambda-u)\varphi=0</math> | * <math>\varphi_{xx}+(\lambda-u)\varphi=0</math> | ||
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| + | <h5>example</h5> | ||
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| + | \[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 7일 (월) 10:52 판
introduction
- \(\varphi_{xx}+(\lambda-u)\varphi=0\)
- discrete spectrum \(\lambda<0\)
- continuous spectrum \(\lambda>0\)
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)
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- http://ncatlab.org/nlab/show/HomePage
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