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arXiv:0802.2606 · Journal of Physics A Mathematical and Theoretical

Two kinds of iterative solutions for generalized sombrero-shaped potential inN-dimensional space

Zhao Wei-Qin

Published May 15, 2008• 0 citations
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Abstract

Based on two different iteration procedures the groundstate wavefunctions and energies for N -dimensional generalized Sombrero-shaped potentials are solved. Two kinds of trial functions for the iteration procedure are defined. The iterative solutions converge nicely on consistent results for different choices of iteration procedures and trial functions.

DOI
10.1088/1751-8113/41/23/235302

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Based on two different iteration procedures the groundstate wavefunctions and energies for N -dimensional generalized Sombrero-shaped potentials are solved. Two kinds of trial functions for the iteration procedure are defined. The iterative solutions converge nicely on consistent results for different choices of iteration procedures and trial functions.
Iterative Solution for Generalized Sombrero-shaped Potential in NNN-dimensional Space
An explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with generalized NNN-dimensional Sombrero-shaped potential is presented. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameters are discussed.
The energy function E( lambda ) of a quantum system with Hamiltonian H( lambda )=H 0 + lambda H 1 is determined by an analytical iterative procedure which yields a rich variety of functional forms. The wavefunction iterates include the solutions of Rayleigh-Schrodinger perturbation theory as well as some additional functions, all of which may be obtained sequentially by standard analytical techniques. At each step, an arbitrary ( lambda -dependent) constant may be chosen freely so as to improve the results of low-order iterates, thereby enhancing the convergence of the procedure.