A method is proposed for the construction of the basis functions in problems with bounded potentials. On the basis of a modified variational method, eigenfunctions and energy levels are obtained for a 2D quantum ring situated in a uniform magnetic field. The case of a coordinate-bounded domain is considered. The resulting basis functions can be used to model the time dynamics of the 2D quantum ring electron wave functions in a finite-size domain.

Keywords: variational method, method of physical-factor splitting, basis functions, Schroedinger equation, 2D quantum ring

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