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Title: Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
Authors:
 [1] ;  [2]
  1. West University of Timişoara, V. Pârvan 4, Timişoara 300223 (Romania)
  2. Politehnica University of Timişoara, Traian Lalescu 2, Timişoara 300223 (Romania)
Publication Date:
OSTI Identifier:
22479559
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EIGENFUNCTIONS; EIGENVALUES; EXACT SOLUTIONS; HAMILTONIANS; METASTABLE STATES; POTENTIALS; SCHROEDINGER EQUATION