"Quantum scattering"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
Pythagoras0 (토론 | 기여) |
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(사용자 2명의 중간 판 14개는 보이지 않습니다) | |||
1번째 줄: | 1번째 줄: | ||
− | ==introduction | + | ==introduction== |
* <math>\varphi_{xx}+(\lambda-u)\varphi=0</math> | * <math>\varphi_{xx}+(\lambda-u)\varphi=0</math> | ||
− | * discrete | + | * discrete spectrum <math>\lambda<0</math> |
− | * continuous | + | * 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)] | * 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]] |
+ | :<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 | ||
− | + | ||
− | + | ==potential scattering== | |
− | |||
− | |||
− | |||
− | |||
− | |||
− | ==potential scattering | ||
<math>r=t-1</math> | <math>r=t-1</math> | ||
33번째 줄: | 35번째 줄: | ||
<math>|r|^2+|t|^2=1</math> | <math>|r|^2+|t|^2=1</math> | ||
− | + | ||
− | + | ||
− | ==delta potential example | + | ==delta potential example== |
* [[delta potential scattering]] | * [[delta potential scattering]] | ||
− | + | ||
− | + | ||
− | ==harmonic oscillator | + | ==harmonic oscillator== |
* [[harmonic oscillator in quantum mechanics]] | * [[harmonic oscillator in quantum mechanics]] | ||
− | + | ||
− | + | ||
− | ==sech potential example | + | ==sech potential example== |
* [[sech potential example]] | * [[sech potential example]] | ||
− | |||
− | |||
− | |||
− | |||
− | + | ==related items== | |
− | |||
− | |||
− | |||
− | ==related items | ||
* [[inverse scattering method]] | * [[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] | |
− | + | * [http://en.wikipedia.org/wiki/Spectrum_%28functional_analysis%29 http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)] | |
− | * [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/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 | ||
+ | [[분류:physics]] | ||
+ | [[분류:math and physics]] | ||
+ | [[분류:migrate]] | ||
+ | |||
+ | ==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'}]