In Griffith's defense I thought it best to include the text that I left out in my previous post
The following is from Griffith's introduction to Quantum Mechanics"It's close, but the sign is wrong, and there's an unwanted boundary term. The sign is easily disposed of: ## \hat{D} ## itself is...
I found a solution in David Griffith's Introduction to Quantum Mechanics 1995 p97 where he asks "Is the derivative operator Hermitian?"
define the derivative operator as
$$ \hat{D}=\frac{\partial }{\partial R} $$
using integration by parts
$$ \left\langle \psi ^*|\hat{D} \psi \right\rangle...
I'm working from Durstberger's Thesis on GEOMETRIC PHASES IN QUANTUM THEORY
http://physics.gu.se/~tfkhj/Durstberger.pdf
equation (2.2.9) in the section on the derivation of the Geometric Phase.
Yes sorry, I should have written n(R(t)) as a basis of eigenstates
<n(R)|∇R|n(R)> = 1/R
so does this make sense, in that the gradient ∇R is the operator? I'm trying to understand Berry's derivation of the Geometric Phase.
And can I take this even further as a second order gradient...
I'm trying to understand gradient as an operator in Bra-Ket notation, does the following make sense?
<ψ|∇R |ψ> = 1/R
where ∇R is the gradient operator. I mean do the ψ simply fall off in this case?
Equally would it make any sense to use R as the wave function?
<R|∇R |R> = 1/R