# 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

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

## Potential energy

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

## Reduced Planck constant

Unit
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

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

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