CCL: Classic analog of quantum mechanics when dealing with Hamiltonian
- From: "Alma Chen" <LQChen^^^protonmail.com>
- Subject: CCL: Classic analog of quantum mechanics when dealing with
- 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?