Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and Pascual Jordan developed matrix mechanics and the Austrian physicist Erwin Schrödinger invented wave mechanics and the non-relativistic Schrödinger equation as an approximation of the generalised case of de Broglie's theory. Schrödinger subsequently showed that the two approaches were equivalent. The first applications of quantum mechanics to physical systems were the algebraic determination of the hydrogen spectrum by Wolfgang Pauli and the treatment of diatomic molecules by Lucy Mensing.