Variational solution for particle in a regular tetrahedron

An accurate variational computation is carried out for a particle in a regular-tetrahedral box, a problem for which the Schrödinger equation cannot be solved in closed form. The ground-state energy is approximated by E 0 = 18.15 ℏ 2 / mV 2 / 3 , where V is the volume of the tetrahedron. A conjecture on the energies of particles in other regular polyhedra is proposed.