January 2013
Beginner to intermediate
336 pages
5h 35m
English
Content preview from Quantum Physics For Dummies, Revised Edition
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Chapter 5
Working with Angular Momentum on the Quantum Level
In This Chapter
Angular momentum
Angular momentum and the Hamiltonian
Matrix representation of angular momentum
Eigenfunctions of angular momentum
In classical mechanics, you may measure angular momentum by attaching a golf ball to a string and whirling it over your head. In quantum mechanics, think in terms of a single molecule made up of two bound atoms rotating around each other. That’s the level at which quantum mechanical effects become noticeable. And at that level, it turns out that angular momentum is quantized. And since that has tangible results in many cases, such as the spectrum of excited atoms, it’s an important topic.
Besides having kinetic and potential energy, particles can also have rotational energy. Here’s what the Hamiltonian (total energy — see Chapter 4) looks like:
Here, L is the angular momentum operator and I is the rotation moment of inertia. What are the eigenstates of angular momentum? If L ...
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