"Quantum scattering"의 두 판 사이의 차이
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+ | ==메타데이터== | ||
+ | ===위키데이터=== | ||
+ | * ID : [https://www.wikidata.org/wiki/Q2381860 Q2381860] | ||
+ | ===Spacy 패턴 목록=== | ||
+ | * [{'LOWER': 'delta'}, {'LEMMA': 'potential'}] |
2021년 2월 17일 (수) 03:03 기준 최신판
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
encyclopedia
- http://en.wikipedia.org/wiki/Schrödinger_equation
- http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)
- http://en.wikipedia.org/wiki/Rectangular_potential_barrier
- http://en.wikipedia.org/wiki/Step_potential
메타데이터
위키데이터
- ID : Q2381860
Spacy 패턴 목록
- [{'LOWER': 'delta'}, {'LEMMA': 'potential'}]