Recent content by Elvex

It's a simple arithmetic mistake... you didn't square the binomial correctly in... (2 - 1.5v_2f) ^ 2 the cross term is -6v_2f not -3v_2f.

The metric tensor has the property of converting covariant to contravariant and vice versa depending on whether it is had subscript or superscript indices. It's not even necessary to understand what covariant and contravariant really mean because einstein notation can be memorized via a set of...

OK, so for the first integral. I have a feeling that I need to change the limits of integration because once I get to k values that exceed the Fermi-Energy, the integrand goes to zero, so setting the upper limit to a specific k value will ensure convergence as well. Oh ok, this is the probably...

Homework Statement Evaluate the integrals (eqns 5.108 and 5.109) for the case of identical fermions at absolute zero. Homework Equations 5.108 N=\frac{V}{2\pi^{2}}\int_{0}^{\infty}\frac{k^2}{e^{[(\hbar^{2}k^{2}/2m)-\mu]/kT}+1}dk 5.109...

Ok so I missed the obvious step of solving for the boundary conditions by simply plugging in x= 0 into my y(x) and dy/dx equations so y(0) = 1 and dy(0)/dx = -1 This is what I got from my sketchy inspection method prior to this. I know the answer now, but I still don't know how to show it will...

Volterra Eqn of 2nd Kind --> DEQ Homework Statement I need to convert y(x) = 1 - x + int[dt(x-t)y(t)] from 0 to x to a differential equation with the appropriate boundary conditions. The Attempt at a Solution OK I just had a problem converting a DEQ into an integral equation so...

The brute force method, usually a method of last resort is the method of frobenius. The problem is you'll generate infinite series solutions which rarely have a closed form. The method is necessary for laplaces equation in cylindrical and spherical coordinates.

No they don't, it's a pendulum in harmonic oscillation, so you can say its angular frequency is simply sqrt(g/L), then solve for (1/2)hw

I got it, I had to set the constraint force to zero, or my lagrange multiplier really cause the gradient of my constraint is trivial in setting F = 0. I then dropped the E term cause E = 0 in this case, U defined as being negative... and then got a term with a's and n's = 1, which can only be...

Homework Statement Consider a point mass m moving under the influence of the gravitational force F= -mg e_y . The mass is constrained to slide along a given curve y= f(x) in the x-y plane. You may set z=0 from the start and consider two dimensional motion. c) A Skier descends a slope with...

* implies time derivative, _i and _j are indices. Homework Statement Consider a Particle of mass m and charge q acted on by electric and magnetic fields E(x,t) and B(x,t). these fields can be described in therms of the scalar and vector potentials PHI(x,t) and A(x,t) for which E= -...