Phy5645/AngularMomentumExercise

From PhyWiki
Jump to navigation Jump to search

In quantum mechanics,

and

The angle between and the axis is given by

To make as small as possible, must be at its maximum value,

Therefore, the minimum angle is given by

or by

We now solve to find

Since will be very large, we make the approximation, so that Because is large, we see that is small, and thus we may make the approximation,

If we now substitute in and we obtain

This is the smallest angle that can make with the axis in the case of the Earth going around the sun.

In the case of a quantum particle with , we must use the exact expression for the angle.

which gives us

This is the smallest angle that the angular momentum vector of a particle with can make with the axis. This angle is much larger than that for the Earth orbiting the sun, as we would expect.

Back to Orbital Angular Momentum Eigenfunctions