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.
On the Raleigh-Ritz variational method. Non-orthogonal basis set
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We overview the main equations of the Rayleigh-Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.
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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.