Theoretical Physics, Second Edition by A. S. Kompaneyets

Author:A. S. Kompaneyets
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2013-03-26T16:00:00+00:00

We shall verify this:

because and are, of course, commutative. Let us add to the right-hand side of the last equality, and subtract from it the combinations and ; we take and outside the brackets, once on the right and another time on the left. Then we obtain

Here we have made use of the commutation rules (29.33)-(29.35). The eigenvalue of M2 will be found in the following section.

Exercises

1) Find the commutations, of

2) Write down the Cartesian projections of momentum in spherical coordinates.

Spherical coordinates are expressed in terms of Cartesian coordinates in the following manner [see (3.5), (3,7), (3.8)]:

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