M.L. Glasser

New isospectral oscillator potentials

Abstract Super-supersymmetric quantum mechanics arises if a second-order differential operator A † intertwines two different Hamiltonians H, H , i.e. H A † = A † H . This technique is used to generate a 2-parameter family of strictly isospectral oscillator potentials embracing the Abraham-Moses case. As a by-product, a 1-parameter family of potentials isospectral to the oscillator, except for the level of the first excited state, is derived.

Second virial coefficient for a Lennard-Jones (2n−n) system in d dimensions and confined to a nanotube surface

Abstract This Letter compares the second virial coefficient for an imperfect gas subject to a 2 n − n interparticle potential in any dimension d between 1 and 2 with that for a gas confined to the surface of a nanotube.

Information-theoretic aspects of friction in the quantum mechanics of an interacting two-electron harmonic atom

In the standard prescriptions (Albrecht in Phys Lett 56B:127, 1975; Hasse in J Math Phys 16:2005, 1975), nonlinear potentials were proposed to introduce a Hermitian potential operator into a Hamiltonian in order to consider quantized friction at the Schrödinger wave-function level. However, this route to understanding quantized friction is not unique. Thus, motivated by important sub-questions put forward by Albrecht and Hasse in the works cited above on the proper choice of parameters introduced in the proposed potentials, we investigate here the information-theoretic aspect of friction using an exact stationary solution for a two-particle interacting one-dimensional oscillator model atom. Specifically, we calculate the change in the diagonal entropy with respect to the well-documented frictionless case, and analyze its parameter-dependence.

Quantum mechanics of a simulated trihydrogen dication

The Schroedinger equation is solved exactly within the Born–Oppenheimer approximation for a simulacrum of the

Analytic structure of ground-state energies and wave functions for the inhomogeneous electron liquid in non-relativistic He-like atomic ions with nuclear charge Ze

H_3^{2+}

Periodic orbits generated from conformal mappings

H32+-ion. The ion is assumed to form an isosceles triangle and the ground state energy is obtained over its geometrical parameter space. No multi-center molecular integrations are required. We indicate how the approximation to the actual molecule can be improved systematically.

Spatial dependence of the RKKY interaction in a semi-infinite d-dimensional medium

Bruch, in early work, treated a spatially free Moshinsky atom with four parallel-spin electrons interacting harmonically. Here we add a harmonic external potential, having an unrelated spring constant