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pellman

- 684

- 5

Thus electrons in an atom have definite energy levels. They also have orbits of discrete angular momentum. But what about free particles?

One might think angular momentum for free particles would also be continuous. But any wavefunction can be expressed as a superposition of spherical harmonics with integer (m,l). Measuring the angular momentum amounts to reduction to a single spherical harmonic and yielding [tex]m\hbar[/tex] with m of the associated spherical harmonic.

Do I have this right? And is this because the range of angles if bounded whether a particle is bounded or not, while momentum and energy for a free particle are unbounded?