ENERGY EIGENVALUES AND EIGENVECTORS FOR BOUND QUANTUM-SYSTEMS USING PARAMETRIC EQUATIONS OF MOTION
DSpace at IIT Bombay
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Title |
ENERGY EIGENVALUES AND EIGENVECTORS FOR BOUND QUANTUM-SYSTEMS USING PARAMETRIC EQUATIONS OF MOTION
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Creator |
MAZZIOTTI, DA
MISHRA, MK RABITZ, HA |
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Description |
This paper considers the solution of a family of Schrodinger equations, characterized by one or more continuous parameters in the Hamiltonian. From a solution of the Schrodinger equation at initial parameter values all other solutions may be obtained by integrating a set of ordinary differential equations in the parameter space of the quantum system. Specifically, the parametric equations for energy eigenvalues and eigenstates are explored. Existing parametric equations are generalized to include nonlinear parameters in the Hamiltonian and systems with degenerate eigenstates. The connections between this method and more traditional methods like perturbation theory and the variational principle are examined. The method is illustrated with the study of the vibrational energies of hydrogen fluoride calculated by deforming continuously the solutions of a harmonic oscillator to those of a Morse oscillator. In another example several coupled diatomic electronic states are considered where the deformation parameter is the bond length. It is demonstrated that no modification of the method is required to treat degeneracies or avoided level crossings.
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Publisher |
AMER CHEMICAL SOC
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Date |
2011-07-14T01:17:48Z
2011-12-26T12:47:29Z 2011-12-27T05:35:02Z 2011-07-14T01:17:48Z 2011-12-26T12:47:29Z 2011-12-27T05:35:02Z 1995 |
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Type |
Article
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Identifier |
JOURNAL OF PHYSICAL CHEMISTRY, 99(1), 112-117
0022-3654 http://dx.doi.org/10.1021/j100001a020 http://dspace.library.iitb.ac.in/xmlui/handle/10054/3821 http://hdl.handle.net/10054/3821 |
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Language |
en
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