Approximate Solutions for Important Model Systems

  • Hans Lüth
Part of the Graduate Texts in Physics book series (GTP)


The most important approximation methods for the solution of the single particle Schrödinger equation are described in this chapter. In particular, the WKB approximation for particle propagation in weak potentials, the variational method, time independent and time dependent perturbation theory including Fermi’s Golden Rule as well as the rotating wave approximation are considered together with application examples, preferentially from interface and nanophysics. The rotating wave approximation for a 2-level system is applied to nuclear magnetic resonance and its application in chemistry, biology and medicine. Scattering theory is treated in Born approximation and applied to Coulomb scattering of electrons and to particle scattering from crystals, surfaces and nanostructures. Inelastic scattering is described in connection with vibrations of an adsorbed molecule.


Ground State Energy Nuclear Magnetic Resonance Signal Scattered Particle Transition Matrix Element Ground State Wave Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hans Lüth
    • 1
  1. 1.Forschungszentrum Jülich GmbH, Peter Grünberg Institut (PGI)PGI-9: Semiconductor Nanoelectronics and Jülich Aachen Research Alliance (JARA)JülichGermany

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