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

$$ \nabla^2 $$

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 $$ \mathrm{J} $$

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 $$ \mathrm{Js} $$

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 $$ \mathrm{kg} $$

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

You must have JavaScript enabled to use this form.

Hey! I am Alexander FufaeV

I have a degree in physics and I wrote this content. It's important to me that you are satisfied when you come here to get your questions answered and problems solved. But since I don't have a crystal ball, I depend on your feedback. That way I can eliminate mistakes and improve this content so that other visitors can benefit from your feedback.

How satisfied are you?

Very nice!

If there is anything you would like to see improved, please send me a message below. I would be very happy if you support the project.

Hmm...

Would you mind telling me what you were missing? Or what you didn't like? I take every feedback to heart and will adapt and improve the content.

What's the trouble?

Do not be disappointed, I can certainly help you. Just send me a message what you actually wanted to find here or what you don't like. I really take your feedback seriously and will revise this content. If you are very disappointed, explain your concern in the feedback and leave your email and I will try to help you personally.