# 4: Quantum Mechanics in Multiple Dimensions


• 4.1: Expanding to Three Dimensions
We look at a few of the differences we encounter when we increase the number of spatial dimension for our Hilbert Space from one to three.
• 4.2: Cartesian Symmetry
We begin our work in three dimensions by examining how to handle quantum systems that are best described in cartesian coordinates.
• 4.3: Spherical Symmetry
We continue our discussion of dealing with three dimensions, this time looking at how to handle quantum systems that are best described in spherical coordinates.
• 4.4: Physical Meaning of Angular Quantum Numbers
We take a closer look at the three quantum numbers we found for the separable stationary-state solutions to the Schrödinger equation, make links to physical quantities and discuss how these exhibit distinctive "quantum" behavior.

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