Studies on some singular potentials in quantum mechanics

Abstract

A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization. Applications have been made to calculate the energies, densities and expectation values for two singular potentials of physical interest, {\em viz.,} (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of $\ell =8$ and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in the light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately.

References in corpus (3)

• Calculation of the spiked harmonic oscillators through a generalized pseudospectral method
• Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudospectral method
• Studies on the hollow states of atomic lithium by a density functional approach

Cited by in corpus (11)

• Spherically confined isotropic harmonic oscillator
• Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential
• Representation reduction and solution space contraction in quasi-exactly solvable systems
• Studies on bound-state spectra of Manning-Rosen potential
• Spectroscopic study of some diatomic molecules via the proper quantization rule
• Bound state spectra of the 3D rational potential
• Information-entropic measures for non-zero l states of confined hydrogen-like ions
• Confined H${}^{-}$ ion within a density functional framework
• Ground and excited states of Li${}^{-}$, Be${}^{-}$ through a density-based approach
• Studies on the bound-state spectrum of hyperbolic potential
• Information analysis in free and confined harmonic oscillator