1
vote
1answer
48 views

Why is the movement of electrons random in electric field?

Suppose an uncharged conductor is present isolated and there is no net electric field applied. Then by assumption we have the motion of electrons random,i.e. isotropic. But now suppose there is a ...
1
vote
3answers
140 views

Intuition/derivation behind the probability current definition

The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain ...
1
vote
1answer
176 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
72 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
239 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
426 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
538 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 ...