Recent content by bigevil

n only has physical meaning for positive values because if you evaluate the energy eigenfunctions, you find that E_n = \frac{n^2 \pi^2 \hbar^2}{2ma^2} Mathematically, at least, it is unnecessary for n to be less than 0. Going by this equation, E0 is by definition the lowest possible energy...

Ok, but L is a constant and having amended that, it doesn't make the final integral any more correct. The ln form of the last equation is still clearly wrong.

Homework Statement Find the capacitance of the parallel plate capacitor with 2 dielectrics below. Given that the parallel plate capacitor has area A = WL and the separation between plates is d. The Attempt at a Solution My method is to use integration. First solve for two small...

Homework Statement For my lab work, I have created a theoretical model that goes something like: T = \sqrt{\frac{ks^2}{x \sin \theta \cos^2\theta}} where k is a constant, and the variables to be differentiated are x, theta and s. How do I find the error of T? I can find the errors of x and...

Homework Statement Two masses, A and B, lie on a frictionless table. They are attached to either end of a light rope of length l which passes around a pulley of negligible mass. The pulley is attached to a rope connected to a hanging mass, C. We are supposed to find the accelerations...

Count Iblis, if I am getting you right, to sum up your method: the Laplacian of f is a scalar. Then, since scalars are invariant under rotation of axes, the Laplacian is invariant under rotation of axes. Would it be sufficient to leave it as that, or would I need to prove it a bit more rigorously?

Homework Statement \frac{dy}{dx} = \frac{cosh x cos y + cosh y sin x}{sinh x sin y - sinh y sin x} I'm really stuck at this one. I don't even know where to start, but I hope that a substitution (ie u = f(x,y)) might be able to put this in a separable form. Any hints please?? Other roads: 1...

Thanks Chip. Count Iblis, ok, I understand a), but what's the vector F? (Do you mean nabla f?) After all I only have scalar function f. How do I proceed from there? Thanks.

Homework Statement A scalar function can be represented as a position on the x-y plane, or on the u-v plane, where u and v are axes rotated by θ from the x and y axes. Prove that the 2-dimensional \nabla^2 operator is invariant under a rotation of axes. ie, \frac{\partial^2 f}{\partial...

Homework Statement The Attempt at a Solution Ok, first part, no problem, second part (steady state), solved in another thread. Both are pretty tedious, but doable. However, I am quite stumped by the third part of this problem (V = V_o sin wt) . The second part of the problem...

Yes, I think so, tim, thanks =)

Homework Statement Question and part 1 as above. The second part involves solving this equation where L = 8R^2 C. The system is kept in steady state by maintaining V(t) = -Q/C (constant). V(t) is then set to 0 at t=0. It also says "Note that V(t)=0 for t>0 and that appropriate initial...

Homework Statement (This is a truncated question.) The electric field of a circular sheet of charge of radius a and surface charge density sigma and distance x away from the centre of the sheet is E = \frac{\sigma}{2 \epsilon_0} [1 - \frac{x}{\sqrt{x^2 + a^2}}] Prove that for x > 0...

I've got an older edition (ca 1995!) Nick. It's weird because Griffiths does a few examples (ie, expand a+ a-, etc) with the operator that I stated at the beginning. I didn't know about the Hermitian part. But this particular question, which I don't think is in newer editions (I checked)...

Homework Statement This is problem 2.11 from Griffith's QM textbook under the harmonic oscillator section. Show that the lowering operator cannot generate a state of infinite norm, ie, \int | a_{-} \psi |^2 < \infty Homework Equations This isn't so hard, except that I consistently get the...