1. The problem statement, all variables and given/known data Due to the radial symmetry of the Hamiltonian, H=-(ħ2/2m)∇2+k(x^2+y^2+z^2)/2 it should be possible to express stationary solutions to schrodinger's wave equation as eigenfunctions of the angular momentum operators L2 and Lz, where L2=-ħ2[1/sin(Θ)(d/dΘ)(sin(Θ)d/dΘ+1/sin2(Θ)d2/dΦ2 Lz=-iħd/dΦ for this radially symmetric system, what are the three lowest energy stationary states that are eigenfunctions of L2 and Lz, with eigenvalues of 0 and 0, respectively? 2. Relevant equations in a previous problem we solved for the 3D stationary states of the harmonic oscillator using seperation of variables and got that Ψnx,ny,nz(x,y,z)=ψnx(x)ψny(y)ψnz(z) also relevant is the solution to the 1D harmonic oscillator: ψ(y)=NnHn(y)e(-1/2∝y2 3. The attempt at a solution Based off of a hint given by one of my GSI's, I was told to begin by taking some of the solutions for the lowest energy stationary states and then convert these solutions to polar coordinates, and then try to manipulate them to look like one the spherical harmonics functions. Following this hint I took the ground state solution, which turned out to be : Ψ000=N03e(1/2)r2, which can be manipulated to look like the first spherical harmonic function, and will have eigenvalues of 0 and 0 when both of the given angular momentum operators are applied, but I'm at a loss as far as finding the other two stationary states, given that all of the other stationary states that I have tried have led to nonzero eigenvalues for one of the two operators. Any help or hints would be appreciated.