I found the answer: effective mass is only useful near the top or bottom of the band, where the dispersion is nearly quadratic, and hence this can be thought of as a free particle with effective mass ( E_free = h^2 k^2/(2m*) ).
After reading another book, I think I understood how conduction...
Hello, I have a question about conduction in metals.
I guess you all know a common pedagogical picture where an electron bands are drawn as ~ cosine curves in 1D or E_0 - cos(k_x) - cos(k_y) in 2D.
Now, in metals , we were told that the Fermi surface passes through the band. Therefore...
Homework Statement
http://img42.imageshack.us/img42/1082/clipboard01lx.jpg
Homework Equations
(see solution)
The Attempt at a Solution
I literary just spent 5 hours trying to apply those boundary conditions, trying exponentials, sines, cosines, hyperbolic function etc... I...
Sorry, I'm a bit confused about solving Schrodinger equation now. Here is my attempt:
http://img691.imageshack.us/img691/9438/72723108.jpg
I used separation of variables and the part that leads to Schrodinger Time Independent equation is ok, but the other part, which involves functions of...
Oh right, I actually just drew a picture in my notes randomly: a dotted curve and a few arrows touching that curve, saying that: Schrodinger equation kinda "picks" a state-vector "path" from Hilbert space(it tells which arrow is next after another, where arrows represent functions |psi(t1)>,|...
We are half-way through the course, so I bet it will refine itself before the exams :)
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So, bases that we can choose to express \left|\Psi\left(t\right)\right\rangle are really physical quantities that can change for that system, so when we have a particle in space, e.g. accelerated...
That's excellent! it's all starting to make sense now. I'll definitely write these down in my summary notes.
By the way, did you have a chance to read my thoughts on a particular example (handwritten picture?) Are they ok-ish for that particular example? here is the link again...
Well actually, now that I tried this discrete case, can I actually express a general state |psi(t)> as \left|\Psi\left(t\right)\right\rangle=\sum\alpha\left|\phi\left(t\right)\right\rangle for a single particle system. That's an infinite linear combination of infinitely many orthonormal square...
Hi, thanks for your replies,especially to peteratcam .I think I get what a wavefunction and a state is for a continuous case of a single particle, but a bit confused about the discreet case of two-state system. Here are my thoughts:
http://img697.imageshack.us/img697/8175/72630741.jpg
I think...
my 1st understanding was that a wavefunction is actually a function of infinitely many spectrums or something, like a function of position, momentum, energy etc... and then we have to "project" it on one of those bases to get it in e.g. position basis psi(x,t) or momentum basis to get psi(p, t)...
Hello, we started Quantum Mechanics last semester, and somehow I manged to do most of the homework during that semester, but now I'm trying to revise it again, and I can't seem to understand the very basics of it, in particular about wavefunctions. Please read this carefully, because you might...