Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom

摘要

The Kravchuk and Meixner polynomials of discrete variable are introduced forthe discrete models of the harmonic oscillator and hydrogen atom. Starting fromRodrigues formula we construct raising and lowering operators, commutation andanticommutation relations. The physical properties of discrete models arefigured out through the equivalence with the continuous models obtained bylimit process.