Solution of the Schrödinger equation for the Morse potential with an infinite barrier at long range

Emanuel F. De Lima, Tak San Ho, Herschel Rabitz

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

The Schrödinger equation is considered for a one-dimensional potential function composed of the Morse oscillator and an infinite barrier at long range. The boundary condition introduced by the barrier implies discretization of the unbound states. The eigenstates and eigenvalues are determined along with the discretization condition and the proper normalization for positive and negative energies. An analysis is presented for a particle in this potential driven by an external field coupled in through a dipole. Analytical formulae are derived for the matrix elements of an exponential and linear dipole function with respect to the eigenstates. Numerical time-dependent solutions to the Schrödinger equation are obtained for a periodic external field.

Original languageEnglish (US)
Article number335303
JournalJournal of Physics A: Mathematical and Theoretical
Volume41
Issue number33
DOIs
StatePublished - Aug 22 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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