Quantum scattering

introduction

• \(\varphi_{xx}+(\lambda-u)\varphi=0\)
• discrete spectrum \(\lambda<0\)
• continuous spectrum \(\lambda>0\)

 

 

harmonic

• harmonic oscillator in quantum mechanics

 

 

continuous spectrum

• \(a(k)e^{-ikx}+b(k)e^{ikx}\)
• a(k) transmission coefficient
• b(k) reflection coefficient

 

 

time independent Schrodinger equation

• Schrodinger equation
  \(E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi\)
  
• \(\varphi_{xx}+(\lambda-u)\varphi=0\)

 

 

example

1. \[Lambda] := -1
   u[x_] := -2 Sech[x]^2
   f[x_] := Sech[x]
   Simplify[D[D[f[x], x], x] + (\[Lambda] - u[x]) f[x]]
   Plot[u[x], {x, -5, 5}]

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• inverse scattering method

 

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• http://eom.springer.de
• http://www.proofwiki.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

 

• 2011년 books and articles
• http://library.nu/search?q=
• http://library.nu/search?q=

 

 

 

 

 

articles

• http://en.wikipedia.org/wiki/Schrödinger_equation
  
• http://en.wikipedia.org/wiki/Spectrum_(functional_analysis)
  
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://www.pdf-search.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/