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- W2078556491 abstract "We study the Schrödinger equation of the hydrogen atom in the (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 analytical exact solution is unknown. We describe the qualitative properties of the energy spectrum, and we propose a semi-analytical method to numerically calculate the eigenenergies (the representation matrix of the Hamiltonian in the Landau basis is analytically calculated and is exactly known). Also, we use a number of useful analytical approximation methods, such as semiclassical approximations, the perturbation method, the variational method and the Taylor power expansion of the potential around the minimum to estimate the ground-state energy and the higher levels." @default.
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- W2078556491 date "2003-07-09" @default.
- W2078556491 modified "2023-09-25" @default.
- W2078556491 title "Two-dimensional hydrogen atom in a strong magnetic field" @default.
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- W2078556491 doi "https://doi.org/10.1088/0305-4470/36/29/304" @default.
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