The Schrodinger equation and stationary states

The master equation for chemical applications of QM is the time-dependent Schrodinger equation  

A system that obeys equation 3.4 is said to be in a stationary state. Chemistry is mostly concerned with stationary states of atomic and molecular systems. 

The language of QM has only a limited correspondence with the language of common objects or even with the specialized language of classical dynamics. In the QM equations for a hydrogen atom, for example, there are no explicit forces or motions, no trajectory of the electron around the nucleus, and indeed there are no material bodies (although there still is mass). The only quantum mechanical reality is a wavefunction that gives the probability of finding the electron at a position x around the nucleus. 

Equation 3.4 is a particular case of a more general rule the only possible (that is, observable) values for a dynamic variable a whose associated operator is A are the solutions of the equation 

The numbers a are called eigenvalues of operator A, and lr is also called the eigenfunction associated with the eigenvalue. Thus, equation 3.4 states that the only observable values for the energy of a system in a stationary state are the eigenvalues of the hamiltonian operator. 

---