"Quantum scattering"의 두 판 사이의 차이

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

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

delta potential scattering

harmonic oscillator

harmonic oscillator in quantum mechanics

sech potential example

sech potential example

related items

inverse scattering method

expositions

encyclopedia

메타데이터

위키데이터

ID : Q2381860

Spacy 패턴 목록

[{'LOWER': 'delta'}, {'LEMMA': 'potential'}]

@@ 2번째 줄: / 2번째 줄: @@
 * <math>\varphi_{xx}+(\lambda-u)\varphi=0</math>
-* discrete spectrum <math>\lambda<0</math>
+* discrete spectrum <math>\lambda<0</math>
-* continuous spectrum <math>\lambda>0</math>
+* continuous spectrum <math>\lambda>0</math>
 * for lists [http://en.wikipedia.org/wiki/Delta_potential_barrier_%28QM%29 http://en.wikipedia.org/wiki/Delta_potential_barrier_(QM)]
 ==time independent Schrodinger equation==
-* [[Schrodinger equation]]<br><math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math><br>
+* [[Schrodinger equation]]
-*  simplified form<br><math>-\varphi_{xx}+u(x)\varphi = \lambda\varphi</math><br><math>\varphi_{xx}+(\lambda-u(x))\varphi=0</math><br>
+:<math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math>
+* simplified form
+:<math>-\varphi_{xx}+u(x)\varphi = \lambda\varphi</math>
+:<math>\varphi_{xx}+(\lambda-u(x))\varphi=0</math>
 ==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
+** <math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math>
+** <math>\varphi \sim \tau(k,t)e^{-ikx}</math> as <math>x\to -\infty</math>
+* <math>\rho(k,t)</math> and <math>\tau(k,t)</math> are called the reflection and transmission coefficient
-* e^{ikx} represents a wave traveling to the right, and e^{−ikx} one traveling to the left
-* e^{−ikx} is incoming wave from the right to the left
-*  reflection and transmission coefficient<br><math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math><br><math>\varphi \sim \tau(k,t)e^{-ikx}</math> as <math>x\to -\infty</math><br><math>\rho(k,t)</math> and <math>\tau(k,t)</math> are called the reflection and transmission coefficient<br>
 ==potential scattering==
@@ 33번째 줄: / 35번째 줄: @@
 <math>|r|^2+|t|^2=1</math>
 ==delta potential example==
@@ 41번째 줄: / 43번째 줄: @@
 * [[delta potential scattering]]
 ==harmonic oscillator==
@@ 49번째 줄: / 51번째 줄: @@
 * [[harmonic oscillator in quantum mechanics]]
 ==sech potential example==
@@ 57번째 줄: / 59번째 줄: @@
 * [[sech potential example]]
-# \[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}]
 ==related items==
@@ 71번째 줄: / 65번째 줄: @@
 * [[inverse scattering method]]
+==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/Schr%C3%B6dinger_equation http://en.wikipedia.org/wiki/Schrödinger_equation]<br>
+* [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)]<br>
+* [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/Step_potential
 [[분류:physics]]
 [[분류:math and physics]]
-[[분류:math and physics]]
+[[분류:migrate]]
+==메타데이터==
+===위키데이터===
+* ID :  [https://www.wikidata.org/wiki/Q2381860 Q2381860]
+===Spacy 패턴 목록===
+* [{'LOWER': 'delta'}, {'LEMMA': 'potential'}]