What is the meaning of current in QM?

[hokhani]

Consider a piece of conductor which is under a DC bias. Solving time-independent Schrödinger equation we have electron wave function which is time-independent and shows special probability for being in each position of the system. How can one say about transmission of electron from one point to another while the electron is always in all the space with the constant (time-independent) probability.

 

[bhobba]

Consider a piece of conductor which is under a DC bias. Solving time-independent Schrödinger equation

You can solve the Schroedinger equation for electrons in a wire?

Charge carrying in conductors is a difficult issue in solid state physics leading to all sorts of weird things such as the absence of electrons behaving like a particle itself - and it just not theory either - see the Hall effect:
http://en.wikipedia.org/wiki/Hall_effect

Thanks
Bill

 

[hokhani]

You can solve the Schrödinger equation for electrons in a wire?

let's assume that we have an ideal situation in which the Schrödinger equation is solvable.

 

[Nugatory]

let's assume that we have an ideal situation in which the Schrödinger equation is solvable.

That's an ideal charged particle hanging out between the two plates of a parallel-plate capacitor. You've got your DC bias, you have your particle free to move, you expect to find solutions in which the expectation value of position over time moves towards one plate or the other over time.