CCL: Classic analog of quantum mechanics when dealing with Hamiltonian oper

 Sent to CCL by: "Alma  Chen" []
 I am reading `The Principles of Quantum Mechanics by Dirac`, in chapter 28
 `Heisenberg's form for the equations of motion`, there is a statement about the
 classic analog about the Hamiltion form between classic mechanics of and
 quantum mechanics. My questions are:
 1. If classic analog means that the Hamiltonian operator is the function of p
 and q(position and mom), then what is the premise of this assumption?
 2. Is there any example of a Hamiltonian that couldn't be expressed as the
 function of p and q?
 3. There is a footnote saying that under Curvilinear coordinates, this
 assumption is NOT right, so I guess that under Curvilinear coordinates, the
 classic Hamiltonian form and quantum Hamiltonian form are NOT the same, is
 there an example of this situation? And why would this happen?