### 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 language | English (US) |
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Article number | 335303 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 33 |

DOIs | |

State | Published - 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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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(33), [335303]. https://doi.org/10.1088/1751-8113/41/33/335303