NUMERICAL COMPUTATION OF THE PSEUDO-GAUSSIAN QUANTUM WELL LEVELS
Pages 48-51
Paul Gravila, Marius Paulescu, Ion I. Cotaescu
Abstract
The potential in a pseudo-Gaussian quantum well behaves asymptotically as Gaussian, but approaches harmonic oscillator (HO) potential near to the origin. A whole family of such potentials can be defined. The quantum problem of finding discrete levels into the pseudo-Gaussian well cannot be solved analytically. First, the generating functional is constructed using symbolic computations. Then, numerical values for the model parameters are allocated and numerical procedures follow to calculate matrix elements of the Hamiltonian operator in the energy basis of HO. Solving these models can be useful for designing new quantum electronic devices.