2.1. Show that the volume element 3N do = (!dp!bp)[I i=1 of the phase space remains invariant under a canonical transformation of the (generalized) coordinates (g, p) to any other set of (generalized) coordinates (Q,P).
2.1. Show that the volume element 3N do = (!dp!bp)[I i=1 of the phase space remains invariant under a canonical transformation of the (generalized) coordinates (g, p) to any other set of (generalized) coordinates (Q,P).
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![2.1. Show that the volume element
3N
do =
Idq;dp;)
i=1
of the phase space remains invariant under a canonical transformation of the (generalized)
coordinates (q, p) to any other set of (generalized) coordinates (Q,P).
[Hint: Before considering the most general transformation of this kind, which is referred to as a
contact transformation, it may be helpful to consider a point transformation– one in which the
new coordinates Q¡ and the old coordinates q; transform only among themselves.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e3775-ae56-4d38-a90c-63585297889c%2F97d663aa-23e4-48c0-84d3-a9b2533769c7%2Fhd165iu_processed.png&w=3840&q=75)
Transcribed Image Text:2.1. Show that the volume element
3N
do =
Idq;dp;)
i=1
of the phase space remains invariant under a canonical transformation of the (generalized)
coordinates (q, p) to any other set of (generalized) coordinates (Q,P).
[Hint: Before considering the most general transformation of this kind, which is referred to as a
contact transformation, it may be helpful to consider a point transformation– one in which the
new coordinates Q¡ and the old coordinates q; transform only among themselves.]
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