Recent content by Matt Chu

I'm not exactly sure why I would integrate by parts again. Integrating by parts once already gives me zero, which is definitely not correct. There must be some mathematical or conceptual mistake that I've made because I don't think it's possible to proceed with what I've done.

Homework Statement I want to prove that ##\frac{\partial \langle x \rangle}{\partial t} = \frac{\langle p_x \rangle}{m}##. Homework Equations $$i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V \Psi$$ The Attempt at a Solution [/B] So...

Is there an issue with the the bounds of integration in this case? I wouldn't think so but I'm not positive.

Homework Statement Given a continuous non-periodic function, its Fourier transform is defined as: $$f(x) = \int_{-\infty}^\infty c(k) e^{ikx} dk, \ \ \ \ \ \ \ \ \ \ \ \ \ c(k) = \frac{1}{2\pi} \int_{-\infty}^\infty f(x) e^{-ikx} dx$$ The problem is proving this is true by evaluating the...

Yeah, just figured that out a few minutes ago.

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

Homework Statement Problem 1.24 (this is unimportant; it's just a different way of calculating the potential energy of a solid cylinder) gives one way of calculating the energy per unit length stored in a solid cylinder with radius a and uniform volume charge density ##\rho##. Calculate the...

Huh, that was easy. Lol

The angle is 90 degrees from the horizontal?

They all extend outwards evenly in every direction.

It would seem that half of the field lines go from 2q to -q. But the angle at which they leave, can that be assumed to be constant regardless of their distance?

That's what I thought, to use a large sphere such that the two charges appear like one point charge and comparing that to the electric field found by using Gauss's law on the individual charges, but that doesn't really give me any relevant information.

Just from the definition of flux it's obvious that the electric field is twice as strong from the charge twice as strong. Therefore there are twice as many lines emerging from the 2q charge as there are going into the -q charge. But that doesn't necessarily tell me how many lines are going from...

That's a part of the question, I guess. I assume it is related to the distance between the charges, but I'm not sure what the relationship is exactly.