\( \mathit{\Psi}(\boldsymbol{r}, t) \) Unit \( \frac{1}{\sqrt{\text{m}^3}} \)

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 in general on the location \( \boldsymbol{r} \), and on the time \( t \).

Laplace-Operator

\( \nabla^2 \) Unit \( \frac{1}{\text{m}^2} \)

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

Potential energy

\( W_{\text{pot}} \) Unit \( \text{J} \)

Potential energy function which gives the potential energy of a quantum mechanical particle at the location \(\boldsymbol{r}\) at the time \(t\). Thus, in general, the potential energy is dependent on location and time.

Imaginary unit

\( i \) Unit \( - \)

Imaginary unit is a complex number for which the following relation holds: \( \textbf{i}^2 ~=~ -1 \).

Reduced Planck constant

\( \hbar \) Unit \( \text{Js} \)

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

\( m \) Unit \( \text{kg} \)

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

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