Adiabatic switching approach to multidimensional supersymmetric quantum mechanics for several excited states |
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Authors: | Chia-Chun Chou Thomas Markovich Donald J Kouri |
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Institution: | 1. Department of Chemistry , University of Houston , Houston , Texas 77204 , USA cchou2@central.uh.edu;3. Departments of Mathematics and Physics , University of Houston , Houston , Texas 77204 , USA;4. Departments of Chemistry, Mathematics, Mechanical Engineering, and Physics , University of Houston , Houston , Texas 77204 , USA |
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Abstract: | We present a time-dependent method for determining several approximate excited-state energies and wave functions using a vectorial approach to multidimensional supersymmetric quantum mechanics. First, a vectorial approach is used to generate the tensor sector two Hamiltonian, which is isospectral with the original scalar sector one Hamiltonian above the ground state of the sector one Hamiltonian. We construct a time-dependent Hamiltonian interpolating between the scalar sector one Hamiltonian and the tensor sector two Hamiltonian. Then, we can adiabatically switch from the ground state of the sector one Hamiltonian to the ground state of the sector two Hamiltonian by solving the time-dependent Schrödinger equation. In addition, by employing an initial wave packet orthogonal to that leading to the ground state of sector two, we also obtain the first-excited state of sector two. Construction of the orthogonal sector one states is trivial due to the tensor nature of sector two. The ground and first-excited states of the sector two Hamiltonian can be used with the charge operator to obtain the first two excited state wave functions of the sector one Hamiltonian. Excellent computational results are obtained for two-dimensional nonseparable degenerate and nondegenerate systems. |
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Keywords: | multidimensional supersymmetric quantum mechanics adiabatic switching excited state anharmonic oscillator |
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