Analytically Solvable 2D Potentials: Bound States
Quantum Physics
2011-10-06 v1 Other Condensed Matter
Abstract
Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix representation of the associated Hamiltonian for few exactly solvable 2D potentials. This enabled us to treat analytically the full Hamiltonian and compute the associated bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we compared our results satisfactorily with those obtained using the Gauss quadrature numerical integration approach.
Keywords
Cite
@article{arxiv.1110.0958,
title = {Analytically Solvable 2D Potentials: Bound States},
author = {S. M. Al-Marzoug and H. Bahlouli and M. S. Abdelmonem},
journal= {arXiv preprint arXiv:1110.0958},
year = {2011}
}
Comments
11 pages, 3 tables. arXiv admin note: substantial text overlap with arXiv:1106.3683