Recent content by iAlexN

I'm new to bra-ket notation and am slightly confused; given an infinite square well with eigenvectors: \phi = \sqrt{2/a}\sin( (n\pi x)/a) And we assume the form: H |φ> = E_n |φ> How would you then represent φ in terms of a column matrix, because that what I thought |φ> represents. Given...

I'm studying periodic boundaries in 1D for which energy gaps occur, i.e. values of the energy which are not allowed, according to the Kronig-Penney model. My question is when these band gaps occur what happens to the wave-function, because it still has to be continuous, so it can't just...

I have lately been trying to understand branch points and branches used for complex, multivalued, functions. From doing questions and reading online, however, I get an unclear view of what branches points are. Take the function: f(z)_a = (z^2+1)^\frac{1}{2} or f(z)_b = log(z-1) Based on...

I agree, the E-field should have the same sign, in this situation I defined the minus y-direction as negative. I get: Fe=−e(-E−vB) = e(E+vB) Fp=e(-E−vB) Supposedly (according to the question) you need not consider the attraction between the electron and the positron, just the Lorentz's...

An electron and a positron are moving in the +x-direction with the same velocity in a crossed electric and magnetic field (the fields are perpendicular). The question states it's impossible to separate them using this configuration. The electric field is pointing in the -y-direction and the...

Given the force (derived from a potential in planar polar coordinates) F(p,w) = 2p+sin(w)e_p+cos(w)e_w Where e_p and e_w are unit vectors How do I calculate the line integral over a circumference that is defined as: p = 2 0 ≤ w ≤ 2pi Using the definition of a line integral \int_0^{2pi} \...

Thanks. Here's my attempt at taking all the partial derivatives, it doesn't quite cancel in the end though. \frac{\partial V}{\partial x} = f(u) - \frac{\partial f(u)}{\partial u} \frac{y}{x} = f(u) - \frac{\partial f(u)}{\partial u} u (The same as you got) \frac{\partial V}{\partial...

If I want to take the derivative of V it would look like this: \frac{\partial V}{\partial x} = \frac{\partial}{\partial x}(xf(u)) But how would you try and evaluate that, because f(u) is some function that depends on x, u=y/x, so you wouldn't get any values out from it? Taking the...

Given V=xf(u) and u = \frac{y}{x} How do you show that: x^2 \frac{\partial^2V}{\partial x^2} + 2xy\frac{\partial^2V}{\partial x\partial y} + y^2 \frac{\partial^2V}{\partial y^2}= 0 My main problem is that I am not sure how to express V in terms of a total differential, because it is a...

Oh, I see. Thanks!

Thank you. It is supposed to be +5 C for the water.

10 g of ice at -20C and 100g of water at +5C is mixed together. How much water and ice will there be once the system reaches equilibrium (assuming no heat is lost)? Specific heat of water and ice: 4.186*10^3, 2.108*10^3 Latent heat of fusion of ice: 333.55*10^3 All in units (kg^{-1} *...

I am trying to solve this integral: \int \frac{x^a-1}{ln(x)} dx (with the interval from 0 to 1). I have tried substitution but I could not find a way to get it to work. Any ideas on how to solve this? Thanks!

Homework Statement A particle with the energy E < V_{0} (V_{0} > 0) moves in the potential V(x) = 0, x<0 ; V(x)= V_{0}, 0<x<d and V(x)= 0, x>d. Measure the probability that the particle will tunnel through the barrier by calculating the absolute value of the ratio squared...

When I factor out e^{E_{1}t/\hbar}: \frac{1}{\sqrt{L}}e^{-iE_{1}t/\hbar}(sin(\frac{pix}{L})+e^{-i(E_{3}-E_{1}t)/\hbar}*sin(\frac{3pix}{L})) However I am not sure how this will make it easier, because the e^{-i(E_{3}-E_{1})t/\hbar} factor is still there. I also tried to separate them to...