- #1
fluidistic
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I am wondering whether electrons have a net motion against an applied constant electric field in a conductor. Intuition tells me that "of course they should", but so far the math has shown me otherwise.
Here are my current thoughts:
1) I cannot rely on the obsolute Drude's model. What's more, electrons aren't like classical particles in an ideal gas. There is no such thing as a drift velocity of the electrons, despite that it is useful to perform many calculations and obtain results that match experiments using that velocity. So it is just a useful concept but not what reality is.
2) I would have simply started with Bloch electrons, with a Bloch Hamiltonian to which I insert the action of an electric field. It turns out it's been somewhat done (of course, obviously) and this leads to Bloch oscillations. I.e. if we consider electrons to have a wavefunction of the form of the one given by Bloch, and if we assume that they have a well definite position and momentum (which is only valid if we leave the realm of QM and fall back to a semiclassical picture), then their motion is an oscillating motion, so that there's no net motion of electrons against the electric field. So this model, which looked the most promising to me to yield a definite answer, goes against intuition. What is this model missing if electrons do indeed posses a net motion against the E field?
How can I mathematically see, using QM theory only (please no semiclassical models), that electrons have a net motion against an applied electric field?
Here are my current thoughts:
1) I cannot rely on the obsolute Drude's model. What's more, electrons aren't like classical particles in an ideal gas. There is no such thing as a drift velocity of the electrons, despite that it is useful to perform many calculations and obtain results that match experiments using that velocity. So it is just a useful concept but not what reality is.
2) I would have simply started with Bloch electrons, with a Bloch Hamiltonian to which I insert the action of an electric field. It turns out it's been somewhat done (of course, obviously) and this leads to Bloch oscillations. I.e. if we consider electrons to have a wavefunction of the form of the one given by Bloch, and if we assume that they have a well definite position and momentum (which is only valid if we leave the realm of QM and fall back to a semiclassical picture), then their motion is an oscillating motion, so that there's no net motion of electrons against the electric field. So this model, which looked the most promising to me to yield a definite answer, goes against intuition. What is this model missing if electrons do indeed posses a net motion against the E field?
How can I mathematically see, using QM theory only (please no semiclassical models), that electrons have a net motion against an applied electric field?