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.
Matrix elements for a generalized spiked harmonic oscillator
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abstract
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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Landau levels in a gravitational field: The Schwarzschild spacetime case
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.