Recent content by jammydav93

I get: dl_j = L/2pi dk_j = L/(2pi*h_bar) dp_j Sorry that must have been a typo, I still seem to have an L^3 term which won't go away though. I now get: = int(dl_x dl_y dl_z) = int ((L/2pi*h_bar)^3 d^3p) = int ((L/2pi*h_bar)^3 4pi*p^2 dp) = int ((L/2pi*h_bar)^3 4pi*E^2/c^3 dE) D(E) =...

Homework Statement Calculate the single particle density of states for massless particles with dispersion E=h_bar ck for a 3D cube of volume V Homework Equations E=pc, p=E/c, dp=dE/c, d^3p = 4pi*p^2 dp k=sqrt(k_x^2+k_y^2+k_z^2) k_j = 2pi/L l_j (j=x,y,z) The Attempt at a Solution I...

\frac{dr}{d\vartheta}=(-rsin(\vartheta), rcos(\vartheta),0) \frac{dr}{dz}=(0,0,1) \frac{dr}{d\vartheta} x \frac{dr}{dz} = (rcos(\vartheta), -rsin(\vartheta),0) A . (\frac{dr}{d\vartheta} x \frac{dr}{dz}) = (x,y,0) . (rcos(\vartheta), -rsin(\vartheta),0) = (rcos(\vartheta)...

Yes sorry I did mean (x,y,0) For the top and bottom face integrals, are they both just trivial as (x,y,0).(0,0,1) = 0 and (x,y,0).(0,0,-1) = 0, or am I doing this wrong? Thanks for the indepth explanation!

Homework Statement Prove the divergence theorem for the vector field A = p = (x,y) and taking the volume V to be the cylinder of radius a with its base centred at the origin, its axis parallel to the z-direction and having height h. I can find the dV side of the equation fine (I think)...

Thanks that was all I needed! Essentially ∅ = arctan(b/a) Thanks for the help!

Homework Statement Rewrite the equation of motion x(t) = 2cos(wt) - 2sin(wt) in the form x(t) = C cos(wt-∅) Homework Equations The Attempt at a Solution I am able to work out the constant C as it is just the magnitude of the sin and cos function, C = (2^2 + 2^2)^1/2 = √8...