Our problem-solving strategy for classical mechanics focused on identifying and using forces. In quantum mechanics we’re interested in energy rather than forces. The critical step in solving a problem in quantum mechanics is to determine the particle’s potential-energy function $U\left(x\right)$. Identifying the interactions that cause a potential energy is the physics of the problem. Once the potential-energy function is known, it is “just mathematics” to solve for the wave function.

The solutions to the Schrödinger equation are the stationary states of the system. Bohr had postulated the existence of stationary states, but he didn’t know how to find them. Now we have a strategy for finding them.

Bohr’s idea of transitions, or quantum jumps, between stationary states remains very important in Schrödinger’s quantum mechanics. The system can jump from one stationary state, characterized by wave function ${\psi }_{\text{i}}\left(x\right)$ and energy $E_{\text{i}}$, to another state, characterized by ${\psi }_{\text{f}}\left(x\right)$ and $E_{\text{f}}$, by emitting or absorbing a photon of frequency

Thus the solutions to the Schrödinger equation will allow us to predict the emission and absorption spectra of a quantum system. These predictions will test the validity of Schrödinger’s theory.