Hi everyone! I am answering this problem which is about the eigenvalues and eigenfunctions of the Hamiltonian given as: H = 5/3(a+a) + 2/3(a^2 + a+^2), where a and a+ are the ladder operators. It was given that a = (x + ip)/√2 and a+ = (x - ip)/√2. Furthermore, x and p satisfies the commutation relation [x,p] = i, i.e., p = -i (d/dx). The question is find the energy eigenvalues and ground state eigenfunction. Is this problem related to the quantum harmonic oscillator? I can't solve it using the usual Hψ = Eψ approach. Thanks a lot!