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

 Sent to CCL by: Yu Zhai [yuzhai*]
 Dear Alma,
I can give an example of your 3rd question if I did not get you in the wrong way.
Watson's Hamiltonian in the field of molecular vibration is not a strict classical-quantal analogue. The Coriolis coupling terms are slightly different...
 You may like to read
James K.G. Watson (1968) Simplification of the molecular vibration-rotation hamiltonian, Molecular Physics, 15:5, 479-490, DOI: 10.1080/00268976800101381
 The description is around eq 17 or so.
 Yu Zhai
 On 6/22/2021 12:53, Alma Chen LQChen- wrote:
 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?>