From owner-chemistry&$at$&ccl.net Tue Jun 22 21:55:00 2021
From: "Yu Zhai yuzhai_+_mail.huiligroup.org" <owner-chemistry]^[server.ccl.net>
To: CCL
Subject: CCL: Classic analog of quantum mechanics when dealing with Hamiltonian oper
Message-Id: <-54415-210622215313-21572-4rueGL44kDMmBcaj4lb2XA]^[server.ccl.net>
X-Original-From: Yu Zhai <yuzhai!=!mail.huiligroup.org>
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Date: Wed, 23 Jun 2021 09:52:59 +0800
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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?>
>