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ENERGY EIGENVALUES AND EIGENVECTORS FOR BOUND QUANTUM-SYSTEMS USING PARAMETRIC EQUATIONS OF MOTION

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Title ENERGY EIGENVALUES AND EIGENVECTORS FOR BOUND QUANTUM-SYSTEMS USING PARAMETRIC EQUATIONS OF MOTION
 
Creator MAZZIOTTI, DA
MISHRA, MK
RABITZ, HA
 
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.
 
Publisher AMER CHEMICAL SOC
 
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
 
Type Article
 
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
 
Language en