From owner-chemistry- at -ccl.net Tue Jun 22 01:25:01 2021
From: "Alma Chen LQChen- -protonmail.com" <owner-chemistry\a/server.ccl.net>
To: CCL
Subject: CCL: Classic analog of quantum mechanics when dealing with Hamiltonian oper
Message-Id: <-54411-210622005346-3663-uohzEWuFj72l/wF/S18Cjw\a/server.ccl.net>
X-Original-From: "Alma  Chen" <LQChen^^^protonmail.com>
Date: Tue, 22 Jun 2021 00:53:44 -0400


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?