Consider a transformation from one set of generalized coordinate and momentum (q, p) to another set (Q, P) denoted by,
Q = pqs; P = qr
where s and r are constants. The transformation is canonical if
1
s = 0 and r = 1
2
s = 2 and r = −1
3
s = 0 and r = −1
4
s = 2 and r = 1