In the first half of 1926, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behavior of a quantum-mechanical wave. The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time. The wave itself is described by a mathematical function known as a "wave function". Schrödinger said that the wave function provides the "means for predicting the probability of measurement results".
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of the electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model.
In May 1926, Schrödinger proved that Heisenbergs matrix mechanics and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom, but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by Wilhelm Wien) "this nonsense about quantum jumps". In the end, Heisenbergs approach won out, and quantum jumps were confirmed.