"Quantum scattering"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 18번째 줄: | 18번째 줄: | ||
==continuous spectrum== | ==continuous spectrum== | ||
| − | * | + | * <math>e^{−ikx}</math> is incoming wave from the right to the left |
| − | * | + | * <math>e^{ikx}</math> represents a wave traveling to the right |
* reflection and transmission coefficient | * reflection and transmission coefficient | ||
** <math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math> | ** <math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math> | ||
| 73번째 줄: | 73번째 줄: | ||
==encyclopedia== | ==encyclopedia== | ||
| − | * [http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation http://en.wikipedia.org/wiki/Schrödinger_equation] | + | * [http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation http://en.wikipedia.org/wiki/Schrödinger_equation] |
| − | * [http://en.wikipedia.org/wiki/Spectrum_%28functional_analysis%29 http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)] | + | * [http://en.wikipedia.org/wiki/Spectrum_%28functional_analysis%29 http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)] |
* http://en.wikipedia.org/wiki/Rectangular_potential_barrier | * http://en.wikipedia.org/wiki/Rectangular_potential_barrier | ||
* http://en.wikipedia.org/wiki/Step_potential | * http://en.wikipedia.org/wiki/Step_potential | ||
2020년 11월 13일 (금) 23:43 판
introduction
- \(\varphi_{xx}+(\lambda-u)\varphi=0\)
- discrete spectrum \(\lambda<0\)
- continuous spectrum \(\lambda>0\)
- for lists http://en.wikipedia.org/wiki/Delta_potential_barrier_(QM)
time independent Schrodinger equation
\[E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi\]
- simplified form
\[-\varphi_{xx}+u(x)\varphi = \lambda\varphi\] \[\varphi_{xx}+(\lambda-u(x))\varphi=0\]
continuous spectrum
- \(e^{−ikx}\) is incoming wave from the right to the left
- \(e^{ikx}\) represents a wave traveling to the right
- reflection and transmission coefficient
- \(\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}\) as \(x\to +\infty\)
- \(\varphi \sim \tau(k,t)e^{-ikx}\) as \(x\to -\infty\)
- \(\rho(k,t)\) and \(\tau(k,t)\) are called the reflection and transmission coefficient
potential scattering
\(r=t-1\)
If t is of the form \(t=\frac{1}{1-ai}\) (real number a), then
\(|r|^2+|t|^2=1\)
delta potential example
harmonic oscillator
sech potential example
expositions
- http://docs.google.com/viewer?a=v&q=cache:nCR9E6bwofAJ:www.rpi.edu/dept/phys/courses/phys410/lct11.pdf+plane+wave+scattering+potential&hl=ko&gl=us&pid=bl&srcid=ADGEEShoNleR3WGnxKKLrDSg_ZNAlytq0EsPPn2ZI2GN79gnfdrNls8jrHdLk68yNQnq4RhMdJdTJ25r52naDFkQcYK9jLXMI7awu5BGD2GvPj05Ky5ZQTu0cKdZVyvI_Ff4rcbrIy7D&sig=AHIEtbSbvDC8BEFTsMXaQRZn04q-bivLnQ
- http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ScatteringTheory.htm