The polynomial quasi-exact solutions for the 2D hydrogen atom in a magnetic field match true eigenstates only at special field strengths, so they are not the full spectrum.
A most misunderstood conditionally-solvable quantum-mechanical model
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In this paper we show that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model. It consists of an eigenvalue equation with seemingly Coulomb, linear and harmonic terms. Here we compare the results derived by those authors with the actual eigenvalues of the models calculated by means of the Ritz variational method.
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On the exact solutions of a two-dimensional hydrogen atom in a constant magnetic field
The polynomial quasi-exact solutions for the 2D hydrogen atom in a magnetic field match true eigenstates only at special field strengths, so they are not the full spectrum.