Referring to define the q variables to be t, x1, y1,z1, x2, y2,z2, the p variables to be p0, p1x ,..

Referring to
define the q variables to be t, x1, y1,z1, x2, y2,z2, the p variables to be p0,
p1x , p1y , p1z,p2x , p2y , p2z the Q variables to be Q0, x, y,z,X, Y, Z and
the P variables to be P0, px , py , pz,Px , Py , Pz, where p = µ(dr/dt) and P =
M(dR/dt).

(a) With the
assumption P0 = p0 and Q0 = q0, prove that the transformation from q, p to Q, P
is canonical.

(b) Show that
this is a canonical transformation of the type discussed and that the standard
quantum substitutions

in the q, p
system imply the quantum substitutions