for example, my prof says that the degeneracy of a 3d harmonic oscillator in the second excited state has a degeneracy of 3. The third excited state has a degeneracy of 3. The fourth excited state has a degeneracy of 1, the fifth excited state has a degeneracy of 6. I don`t understand where...
and what would the eigenspace be? that is my main cocern, setting up the NxN eigenspace as per my op. my prof didnt discuss how to get the values of degeneracy.
So what I do know about degeneracy is that it's the size of an eigenspace in a certain state. How would I go about setting up the eigenspace? Let's say for a particle in the first state with n values nx = 2, ny = 1, nz = 1
Edit: Problem solved please disregard this post
Homework Statement
A particle in the harmonic oscillator potential has the initial wave function \Psi(x, 0) = ∑(from n = 0 to infinity) Cnψn(x) where the ψ(x) are the (normalized) harmonic oscillator eigenfunctions and the coefficients are given...
OH my, rookie mistake LOL. but still, i only get that y''p + yp = 2Acosx - 2Csinx. My logic is telling me to try out yp = (Ax^2 + Bx + C)sinx + (Dx^2 + Ex + F)cosx, based upon my classroom notes. I try this and get
y''p + yp = 2Asinx + 2Dcosx + 2(2Ax+B)cosx -2(2Dx + E)sinx = xsinx
now i...
Homework Statement
y'' + y = xsinx where y(0) = 0 and y'(0) = 1
Homework Equations
yc = C1sinx + C2cosx
The Attempt at a Solution
So my attempt includes the yc which undoubtedly is correct. I now try to solve yp
yp = Axsinx + Bxcosx
y''p = A(2cosx - xsinx) + B(-2sinx -...
t^2 = xF/((1/2)*a) where a = 6.6... Factoring in friction i get a net force of 0.36N in the tangential Velocity direction. i solve for t (sqrt(xF/((1/2)*0.72)) which is 18.7s. 18.7*0.72=velocity, which is 13.5 m/s. (Fnet)r = (0.5*13.5^2)/2 = 91N... 91N/(0.5*2) = w^2... sqrt that and i get...
sorry about that i figured u knew what i was doing with the xF = xI + vI*t + 1/2(a*t^2)... the vI is zero, so i substituted 126m (the circumference of 10 revs) into xF. The force i found was Ft[force along tangential velocity]=3.5cos(20)... I did not factor in a frictional force after this (my...
Homework Statement
A 500 g steel block rotates on a steel table while attached to a 2.0-m-long massless rod. Compressed air fed through the rod is ejected from a Inozzle on the back of the block, exerting a thrust force of 3.5 N. The nozzle is 70 degrees from the radial line, so that the net...