@drmatusek

Split kinetic energy method for quantum systems with competing potentials

, and . Annals of Physics 327 (9): 2061 - 2073 (September 2012)

Abstract

For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such a kind of problems, we develop a general solution scheme based on a new energy dissection idea. Instead of dividing the potential energy into “unperturbed” and “perturbed” terms, a partition of the kinetic energy is performed. By distributing the kinetic energy term in part into each individual potential, the Hamiltonian can be expressed as the sum of the subsystem Hamiltonians with respective competing potentials. The total wavefunction is expanded by using a linear combination of the basis sets of respective subsystem Hamiltonians. We first illustrate the solution procedure using a simple system consisting of a particle under the action of double δ -function potentials. Next, this method is applied to the prototype systems of a charged harmonic oscillator in strong magnetic field and the hydrogen molecule ion. Compared with the usual perturbation approach, this new scheme converges much faster to the exact solutions for both eigenvalues and eigenfunctions. When properly extended, this new solution scheme can be very useful for dealing with strongly coupling quantum systems.

Description

ScienceDirect.com - Annals of Physics - Split kinetic energy method for quantum systems with competing potentials

Links and resources

DOI:
10.1016/j.aop.2012.05.010
URL:
BibTeX key:
Mineo20122061
search on:

Comments and Reviews  
(0)

There is no review or comment yet. You can write one!

Tags


Cite this publication