Recent content by Mentia

Let \vec{f}(x,y,z)=f_x(x,y,z)\hat{x}+f_y(x,y,z)\hat{y}+f_z(x,y,z)\hat{z}. Then \vec{f}\times\vec{f}^\ast =(f_yf_z^\ast -f_y^\ast f_z)\hat{x}+(f_zf_x^\ast -f_z^\ast f_x)\hat{y}+(f_xf_y^\ast -f_x^\ast f_y)\hat{z}=2i\left [ \text{Im}(f_yf_z^\ast)\hat{x} + \text{Im}(f_zf_x^\ast)\hat{y} +...

Is it possible to nontrivially represent the cross product of a vector field \vec{f}(x,y,z) with its conjugate as the gradient of some scalar field \phi(x,y,z)? In other words, can the PDE \vec{\nabla}\phi(x,y,z) = \vec{f}(x,y,z)\times\vec{f}^\ast(x,y,z) be nontrivially (no constant...

What's the difference between a plasmon and the wave that propagates through a wire when you flip a light switch?

Suppose you have a long wire. One end of the wire is close to a very very strong source of electric field. It is my understanding that the electrons responsible for bonding in a metal are also those responsible for conduction. If you have an extreme electric field near to the conductor, and...

In undergrad physics I've learned that the hydrogen atom can capture a photon of the correct energy and bump the electron to a higher energy level. My question is, how close does the photon have to pass to be captured? Does the photon have to hit the electron... ? How does that work? What...

What about a piecewise defined function: f(x) = (x+1)^2 for -inf < x < -1 0 for -1 <= x <= 1 (x-1)^2 for 1 < x < +inf this is continuous and analytic and all those nice things isn't it? Edit: Whoops I'm not doing very well today. 2nd deriv problems...

if you have to prove that gamma (1/2) = sqrt(pi) you should start from the definition of the gamma function and then use polar coordinates, it'll fall right out.

As far as your #4 goes you are totally on the right track. You have to look at what you solve for though. You solved for w = 1154.7. What you want is p.

Hey hey. This is a pretty cool problem I think. What you're doing is calculating the Schwartzchild radius. You can get more info on that from Wikipedia: http://en.wikipedia.org/wiki/Schwarzschild_radius Basically, you set the escape velocity to be the speed of light and then solve for "r"...

Subtle difference Your differentials are perfect. You just took them too far. Dont substitute with x. You want to solve for the energy distribution function in terms of lambda. That way you can take the derivative of the energy distribution function and set to zero to find maximum. Check out...