Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.4, pp.445-456

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.4, pp.445-456

Atoms in Strong Magnetic Fields: Some New Analytic Results.
Marko Robnik and Valery G. Romanovski

We study the Schrödinger equation of the hydrogen atom in (arbitrarily) strong magnetic field in two dimensions, which is an integrable and separable system. The energy spectrum is very interesting as it has infinitely many accumulation points located at the values of the Landau energy levels of a free electron in the uniform magnetic field. In the polar coordinates the canonical (not kinetic!) angular momentum has a precise eigenvalue and we have the one dimensional radial Schrödinger equation which is an ordinary second order differential equation whose analytic exact solution is unknown. We describe the qualitative properties of the energy spectrum, propose a semianalytic method to numerically calculate the eigenenergies (the matrix of the Hamiltonian is exactly known) and use a number of useful analytic approximation methods, such as semiclassical approximations, perturbation method and variational method to estimate the ground state energy and the higher levels.
Key words: hydrogen atom, magnetic fields, Zeeman effect

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