Formula Time independent Schrödinger equation (3d)

Wave function

Three-dimensional probability amplitude, with which the you can calculate the probability for finding a quantum mechanical particle at a certain position. The wave function depends on the location $$\boldsymbol{r}$$.

Laplace operator

The Laplace operator is applied to the wave function. It contains the second partial derivatives with respect to the spatial coordinates:$\nabla^2 ~=~ \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}$

Total energy

Total energy of a quantum mechanical particle described by the stationary state $$\mathit{\Psi}$$.

Potential energy

Potential energy can depend on location $$\boldsymbol{r}$$ in the case of stationary Schrödinger equation, but not on time $$t$$.

Reduced Planck constant

Reduced Planck constant is a natural constant and has the value: $$\hbar ~=~ \frac{h}{2 \pi} ~=~ 1.054 \, 572 ~\cdot~ 10^{-34} \, \text{Js}$$

Mass

Mass of the quantum mechanical particle (e.g. an electron).