Abstract: The motion of a charged particle in the magnetic field is described in many textbooks, however, the charged particle in two-dimensional infinite potential well has been not mentioned yet. In this paper we investigate the energy of charged particle and Landau energy levels with the bound of two-dimensional infinite potential well.

Key words: two- dimensional ring infinite potential well, Pauli equation, Bessel equation, Sturm- Liouville equation, Landau energy