Question

When will be use time independent schrodinger equation?

Answer 1

The time-independent Schrödinger equation is just separation of variables acting on the “true” Schrödinger equation. The eigenvalues (the separation constants) of such equation just so happen to represent the energy of our quantum system. As such, if our interest is solely on the available and accessible states of or system, the time-independent version does just fine. If, however, we seek to model the system’s time evolution, then we need to evoke the time part of the Schrödinger equation.