Quantum-mechanical solution for the double oscillator in a box

Abstract

The quantum-mechanical problem of the double oscillator in a box is solved by diagonalizing the matrix of the Hamiltonian on the basis of the wave functions for the free particle in the box. Perturbative and asymptotic solutions, valid for small- and large-size boxes, respectively, are also obtained. An interpolation between the approximate solutions leads to the construction of Padé-approximant forms for the energy levels that are valid for boxes of any size. A comparison between the exact and the approximate solutions is made in order to ascertain the accuracy and range of validity of each one. Special attention is paid to the lowest levels. © 1981 Società Italiana di Fisica.