Solution of the Schrödinger Equation for Four Specific Problems

  • Rolf E. Hummel


At first we solve the Schrödinger equation for a simple but nevertheless very important case. We consider electrons which propagate freely, that is, in a potential free space in the positive x direction. The potential energy V is then zero and the Schrödinger equation (3.1) assumes the following form:
$$ \frac{{{d^2}\psi }}{{d{x^2}}} + \frac{{2m}}{{{\hbar ^2}}}E\psi = 0$$


Potential Barrier Free Electron Potential Distribution Electron Wave Bloch Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Rolf E. Hummel
    • 1
  1. 1.Department of Materials Science and EngineeringUniversity of FloridaGainesvilleUSA

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