Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 10.4, Problem 10.14P
To determine
The value of
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For Problem 8.16, how do I prove the relations and give the correct expressions?
Statistical Physics. Microcanonical Ensemble.
2.2. (a) Verify explicitly the invariance of the volume element do of the phase space of a single particle
under transformation from the Cartesian coordinates (x,y, z, px, Py, Pz) to the spherical polar
coordinates (r,e,4,Pr.Pe,Po).
(b) The foregoing result seems to contradict the intuitive notion of "equal weights for equal solid
angles," because the factor sine is invisible in the expression for do. Show that if we average
out any physical quantity, whose dependence on po and po comes only through the kinetic
energy of the particle, then as a result of integration over these variables we do indeed recover
the factor sin0 to appear with the subelement (de do).
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