"Quantum scattering"의 두 판 사이의 차이

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==introduction==
  
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* <math>\varphi_{xx}+(\lambda-u)\varphi=0</math>
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* discrete spectrum <math>\lambda<0</math>
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* continuous spectrum <math>\lambda>0</math>
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* for lists [http://en.wikipedia.org/wiki/Delta_potential_barrier_%28QM%29 http://en.wikipedia.org/wiki/Delta_potential_barrier_(QM)]
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==time independent Schrodinger equation==
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* [[Schrodinger equation]]
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:<math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math>
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* simplified form
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:<math>-\varphi_{xx}+u(x)\varphi = \lambda\varphi</math>
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:<math>\varphi_{xx}+(\lambda-u(x))\varphi=0</math>
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==continuous spectrum==
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* <math>e^{−ikx}</math> is incoming wave from the right to the left
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* <math>e^{ikx}</math> represents a wave traveling to the right
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* reflection and transmission coefficient
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** <math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math>
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** <math>\varphi \sim \tau(k,t)e^{-ikx}</math> as <math>x\to -\infty</math>
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* <math>\rho(k,t)</math> and <math>\tau(k,t)</math> are called the reflection and transmission coefficient
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==potential scattering==
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<math>r=t-1</math>
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If t is of the form <math>t=\frac{1}{1-ai}</math> (real number a), then
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<math>|r|^2+|t|^2=1</math>
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==delta potential example==
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* [[delta potential scattering]]
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==harmonic oscillator==
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* [[harmonic oscillator in quantum mechanics]]
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==sech potential example==
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* [[sech potential example]]
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==related items==
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* [[inverse scattering method]]
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==expositions==
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* 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
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* http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ScatteringTheory.htm
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==encyclopedia==
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* [http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation http://en.wikipedia.org/wiki/Schrödinger_equation]
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* [http://en.wikipedia.org/wiki/Spectrum_%28functional_analysis%29 http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)]
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* http://en.wikipedia.org/wiki/Rectangular_potential_barrier
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* http://en.wikipedia.org/wiki/Step_potential
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[[분류:physics]]
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[[분류:math and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q2381860 Q2381860]
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===Spacy 패턴 목록===
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* [{'LOWER': 'delta'}, {'LEMMA': 'potential'}]

2021년 2월 17일 (수) 03:03 기준 최신판

introduction


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


related items


expositions


encyclopedia

메타데이터

위키데이터

Spacy 패턴 목록

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