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Quantum Newtonian cosmology and the biconfluent Heun functions

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arxiv 1502.03071 v2 pith:VGYVNLAR submitted 2015-02-10 gr-qc math-phmath.MP

H. S. Vieira , V. B. Bezerra This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords biconfluentfunctionsheunconstantcosmologicalenergynewtoniancodify
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We obtain the exact solution of the Schr\"odinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the biconfluent function are written explicitly. The energy spectrum which resembles the one corresponding to the isotropic harmonic oscillator is also obtained. The wave functions as well as the energy levels codify the role played by the cosmological constant.

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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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