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Matrix elements for a generalized spiked harmonic oscillator

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arxiv quant-ph/9812048 v1 pith:QMEGWIC6 submitted 1998-12-17 quant-ph math-phmath.MP

Richard L. Hall , Nasser Saad , Attila B. von Keviczky This is my paper · ORCID
classification quant-phmath-phmath.MP
keywords harmonicoscillatorpotentialaguilera-navarroalphaclosed-formdmanearlier
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Closed-form expressions for the singular-potential integrals <m| x^-alpha |n> are obtained with respect to the Gol'dman and Krivchenkov eigenfunctions for the singular potential V(x) = B x^2 + A/x^2, B > 0, A >= 0. These formulas are generalizations of those found earlier by use of the odd solutions of the Schroedinger equation with the harmonic oscillator potential [Aguilera-Navarro et al, J. Math. Phys. 31, 99 (1990)].

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  1. Landau levels in a gravitational field: The Schwarzschild spacetime case

    gr-qc 2019-09 conditional novelty 5.0 of 10

    In Schwarzschild spacetime, a weak gravitational field splits Landau levels by an amount proportional to GMm times the square root of the magnetic field, with explicit Yukawa, power-law, and relativistic corrections derived.

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