Tunneling States of Impurities in Off-Center Potentials with Octahedral Symmetry

Abstract

The tunneling states of an impurity in off-center potentials with O_h-symmetry is investigated. A method of solving the quantum mechanical eigenvalue problem is presented, in which the wave function is expanded in a series of the symmetrized orthonormal set of the basis functions constructed by the eigenstates of a three-dimensional harmonic oscillator. The Schrödinger equation is transformed into a secular equation for the Hamiltonian matrix and solved numerically. The method is applied to a model potential given by V(r)=a(x²+y²+z²)+b(x⁴+y⁴+z⁴)+c(x²y²+y²z²+z²x²), which covers the cases from ⟨100⟩-off-center minimum to ⟨111⟩-off-center minimum continuously by changing the parameter values. The features of the level structure are clarified in connection with the potential shape.