1. The problem statement, all variables and given/known data in the 3rd problem consider a particle with mass m and of potential energy V(x,y,z)=( (mω^2)/2) * [(1+ (2λ/3))*(x^2 +y^2) + (1- (4λ/3))*z^2] where ω , λ are constants ω≥0 , 0≤λ≤3/4 what are the eigenstates of the Hamiltonion and the corresponding energies whats the degeneracy of the ground state λ=0 and the first state λ=3/4 2. Relevant equations 3. The attempt at a solutionok if λ=0 i know that v= 1/2 ω(^2) m (x^2+y^2+z^2) which means the H=Hx+Hy+Hz, and that means E=(nx +ny+nz+3/2) hw and the ground state u have (1.0.0) and (0.1.0). and (0.0.1) and E= 5/2 hw for λ=3/4 V=1/2 mw^2(3/2)(x^2+y^2) so v=3/2 1/2 mw^2(x^2+y^2) so H=Hx+Hy=(nx+ny+1)3/2 h w and the ground state degeneracy is (1.0) (0.1) ?! ( i know i made alot of mistakes :P, but i am EE major and this class is supposed to be introductory quantum) i am not sure about the eigen states, but it looks like a harmonic oscillator so its ground state it should be ψ=N0e^-1/2 ζ ?!!