Exact solution of the schrodinger equation for a particle in a tetrahedral box

Abstract

The authors obtain the exact solution of the Schrodinger equation for a particle confined to (i) an equilateral triangle, (ii) a tetrahedral box with corners (- pi / square root 2,- pi / square root 2,- pi / square root 2), ( pi / square root 2,- pi / square root 2, pi /2); (- pi / square root 2, pi / square root 2, pi /2) and ( pi square root 2, pi / square root 2,- pi /2). The energies are: for (i) E _nl=(8h(cross)² pi ²/9mL²)(n²+l²-ln) where L is the side of the triangle and l, n are distinct non-zero integers and for (ii), E_lmn=(h(cross)²/8m)^∗(3(l²+m²+n²)-2lm-2mn-2nl) where l, m and n are distinct non-zero integers. The wavefunctions have been classified according to the irreducible representation of the corresponding symmetry groups.