Studies on the bound-state spectrum of hyperbolic potential

Abstract

Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n,\ell$ quantum states by solving the relevant non-relativistic Schrödinger equation allowing a non-uniform, optimal spatial discretization. Eigenvalues accurate up to tenth decimal place are reported for a large range of potential parameters; thus covering a wide range of interaction. Excellent agreement with available literature results is observed in all occasions. Special attention is paid for higher states. Some new states are given. Energy variations with respect to parameters in the potential are studied in considerable detail for the first time.

arXiv comment13 pages, 3 figures, 2 tables

References in corpus (9)

• Solving the Schroedinger equation for bound states with Mathematica 3.0
• Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials
• Spherically confined isotropic harmonic oscillator
• The generalized pseudospectral approach to the bound states of Hulthen and Yukawa potentials
• A DPF analysis yields accurate analytic potentials for Li${}_2(a{}^3{\Sigma }_u^{+})$ and Li${}_2(1{}^3{\Sigma }_g^{+})$ that incorporate 3-state mixing near the $1{}^3{\Sigma }_g^{+}$-state asymptote
• Studies on some singular potentials in quantum mechanics
• Bound state spectra of the 3D rational potential
• Approximate analytic solutions of the diatomic molecules in the Schrodinger equation with hyperbolical potentials
• Ground and excited states of Li${}^{-}$, Be${}^{-}$ through a density-based approach

Cited by in corpus (1)

• Formula Method for Bound State Problems