Recent content by DivGradCurl

Hi all, I'm reviewing device physics and I would like to understand how majority and minority carrier concentrations for both N- and P-type substrates change with temperature. My reference, Pierret's Semiconductor Device Fundamentals, has this figure: and I want to generate curves for all...

I have something to add. I think I figured out these questions; please confirm: 1. k-spacing: Looks right on the initial post 2. Number of electrons: N = (2N_a) (2 N_b)(2 N_c) = 8 N_a N_b N_c From the 1D analysis at the edge of the 1st Brillouin zone: n_a \frac{2\pi}{L_a} = \frac{\pi}{a}...

Hi all, I’m brushing up my skills on solid state physics and I have a few questions about crystal lattices: 1. What’s the spacing between allowed kx, ky, and kz states for a lattice of dimensions La x Lb x Lc? My attempt: The spacing is kx, ky, and kz: k_x = \frac{2\pi}{L_a}, \qquad k_y =...

I get you; makes sense now! I also see what you mean by the three linear independent vectors as [1; 0; 0], [0; 1; 0], and [0;0;1]. They give away 3 columns of M. Too bad the system I'm crunching this data through doesn't have that level of direct control, so I need to get as close as possible...

I managed to find a number of the elements by rewriting my Solve[ ] call: And, as you can see above, I'm left with the first column vector within M, i.e. [m11; m21; m31], left to be determined. To be honest, I don't understand why I have those 3 elements left to be determined. Using vector...

Hi, I'm trying to reconstruct the matrix M with Mathematica's Solve[ ]: The vectors are basically (x, y ,z) and (x' , y' , z') coordinates And the data behind this mess is here - shown in (x,y,z) row sets - where the "M4" and "IF" would be like A and B in M*A = B. The data looks linearly...

Hi all, I have this data that can be described by M*A = B, where M is a 3x3 matrix and A and B are 3x1 vectors. Since I know and can collect A and B data, and I have 9 unknowns in the 3x3 matrix, I thought that collecting 9 pairs of A and B vectors would yield the matrix M's coefficients via 9...

Hey thanks for the explanation, jtbell. That makes sense now.

Hi all, I came across this figure in a textbook. Simple stuff, but can get tricky: I don't understand why the sign convention flips upon entering the barrier (region II), but I guess the book is correct and that I should just take it as a fact. If anybody has a reasonable thought to add...

Hi all, I'm trying to understand how to calculate the time dependent expectation value of the atomic dipole moment for a superposition state, and I have a good guess to check with you. Say we have \psi = \frac{1}{\sqrt{2}} \left[ \psi _{100} + \psi _{310} \right] at t = 0. Then, for t > 0: \Psi...

Exactly, subsequent measurements and wavefunuction collapse, giving probability of 1. Thanks

Hi, On (1), thanks for bringing that point up. I guess I should express my solution as \langle |\mathbf{L}| \rangle = \left\langle \sqrt{ \mathbf{L}^2 }\right\rangle which is what it seems to be. On (2), the probabilities are just the modulus squared of the coefficients, which I arbitrarily...

I've just caught my own mistake. Every \hbar in the above posts should be squared. Other than that, I'm assuming it's correct.

Let me bring an additional question, related to the original post with an added twist. If I were to change the wavefunction to, for example \psi = \frac{1}{\sqrt{2}} \psi_{100} + \frac{1}{\sqrt{2}} \psi_{310} and wanted (1) the expectation value of the total angular momentum and (2) the...

Yeah, I see your point. There is a simpler way to approach it. Looks like we're arriving at the same answer either way, which is good. Thanks