## Time independent Schrödinger equation

The Schrödinger equation $$-\frac{\hbar}{i}\frac{\partial\Psi(x,t)}{\partial t}=-\frac{\hbar}{2m}\frac{\partial^{2}\Psi(x,t)}{\partial x^{2}}+V(x,t)\Psi(x,t)$$ involves a state function ($$\Psi$$ wave function) which depends on spatial coordinates and time. For simplicity, let us consider the wave function for a particle in the one-dimensional case. Fortunately, for many applications of chemistry the time-independent Schrödinger equation, which gives rise to stationary states, is sufficient. In this Read More …

## Degeneration in quantum mechanics

Degeneration occurs when two or more independent wave functions have the same eigenvalue. It is said that $$n$$ functions $$f_ {1}, f_ {2,} \ldots, f_ {n}$$ are linearly independent if the condition $$\sum_{i}c_{i}f_{i}=0$$ it is satisfied when all the constants $$c_ {i}$$ are equal to zero. The degree of degeneration of a system is Read More …