Solution of the Radial Schrödinger Equation by the Fox-Goodwin Method

  • Erich W. Schmid
  • Gerhard Spitz
  • Wolfgang Lösch

Abstract

Solving the Schrödinger equation is the central problem of non-relativistic quantum mechanics. A simple case is the study of the motion of a particle without spin in an external potential. The time-independent Schrödinger equation in this case reads
$$ H\psi \left( r \right) = E\psi \left( r \right), $$
(13.1a)
with the Hamilton operator
$$ H = - \frac{{{\hbar ^2}}}{{2m}}\Delta + V\left( r \right). $$
(13.1b)
If the particle is scattered by the potential, the energy E may be given any positive value. If the particle is bound by the potential, E becomes negative and can only take discrete values.

Keywords

Helium Dinates 

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References

  1. 13.1 Apart from a trivial change for V 0 we take the values from B. Buck, H. Friedrich, C. Wheatley: Nucl. Phys. A275, 246 (1977)Google Scholar
  2. 13.2
    B. Alder, S. Fernbach, M. Rothenberg (eds.), Methods in Computational Physics, Vol. 6, Nuclear Physics (Academie Press, New York 1966)Google Scholar
  3. 13.3
    M. Abramowitz, I.A. Stegun (eds.): Handbook oE Mathematieal Functions, 7th ed. (Dover Publications, New York 1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Erich W. Schmid
    • 1
  • Gerhard Spitz
    • 1
  • Wolfgang Lösch
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenFed. Rep. of Germany

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