Undergrad Quantum Mechanics Wave Function in 3D

[Icycub]

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

 

[atyy]

The wave function itself is complex valued, so that's 2 values (real and imaginary values) at each position (x,y,z).

We usually say 3 dimensions, because we mean 3 space dimensions.

 

[vanhees71]

What makes more sense is to visualize $|\psi(\vec{x})|^2$. For a qualitative overview a density plot is nice. Another way are plots of "orbitals", i.e., the places with a probability >some value. See, e.g., the figures in the Wikipedia article for the hydrogen atom in the English and German Wikipedia:

https://en.wikipedia.org/wiki/Hydrogen_atom
https://de.wikipedia.org/wiki/Wasserstoffatom