Computational method for the quantum Hamilton-Jacobi equation: Bound states in one dimension
- Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712 (United States)
An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Moebius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.
- OSTI ID:
- 20864330
- Journal Information:
- Journal of Chemical Physics, Vol. 125, Issue 17; Other Information: DOI: 10.1063/1.2358988; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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