1
vote
1answer
117 views

Electric current in quantum mechanics?

Quick question: I want to find an expression for the (electric) current density of an electron, in quantum mechanics. Either a single electron or a general charge distribution $\rho$. Classically ...
2
votes
0answers
62 views

current density in 1-d

I have a slight problem with the notion of the current density in one dimension. For example the probability current in 1-d given by: $J(x) = -\frac{1}{m} Im(-i\psi^*\partial_x \psi)$ calculation the ...
2
votes
1answer
196 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi ...
4
votes
1answer
334 views

quantum mechanics current operators

How to derive the charge current and the energy current operators in second quantized form in Quantum mechanics ? Also if you could comment in a similar way on the entropy current operator, that will ...
4
votes
1answer
468 views

Relating the variance of the current operator to measurements

(EDIT: Thanks to Nathaniel's comments, I have altered the question to reflect the bits that I am still confused about.) This is a general conceptual question, but for definiteness' sake, imagine a ...