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

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 /9mL 2 )(n 2 +l 2 -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(l 2 +m 2 +n 2 )-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.