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

[Yu Zhai <yuzhai!=!mail.huiligroup.org>]

 Sent to CCL by: Yu Zhai [yuzhai*mail.huiligroup.org]
 Dear Alma,
 Hi.
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.
 Cheers,
 Yu Zhai
 On 6/22/2021 12:53, Alma Chen LQChen- -protonmail.com wrote:
>  Sent to CCL by: "Alma  Chen" [LQChen-#-protonmail.com]
>  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?>