Exact solution for a hydrogen atom in a magnetic field of arbitrary strength

Abstract

An exact solution describing the quantum states of a hydrogen atom in a homogeneous magnetic field of arbitrary strength is obtained in the form of a power series in the radial variable with coefficients being polynomials in the sine of the polar angle. Energy levels and wave functions for the ground state and for several excited states are calculated exactly for the magnetic field varying in the range 0B/(${\mathit{m}}^{2}$${\mathit{e}}^{3}$c/${\mathrm{\ensuremath{\Elzxh}}}^{3}$)\ensuremath{\le}4000. \textcopyright{} 1996 The American Physical Society.