1. The problem statement, all variables and given/known data I'm doing problems for practice in quantum physics. Consider two particles of the mass m in one dimension with coordinates being denoted by x and they are connected by a spring with spring constant k. Suppose that the total momentum of the system is p. Find all possible total energies for the following cases : (1)two particles are different (2)two particles are identical fermions. 2. The attempt at a solution (1) I try to guess the answer... Total energy is the sum of potential and kinetic energy. Now our particles have the same mass and they are one-dimensional. Moreover, they are non-identical. Now potential energy is based on spring constant K therefore V=1/2*K*x^2 . Now considering the harmonic oscillator in classic sense total energy E= T +V Therefore E = P^2/2m + 1/2*mω^2*x^2. considering energy from quantum mechanical point of view, we know P= -iℏ d/dx =p' and x=x' hamiltonian becomes, H= 1/2 p'^2/2m + 1/2*mω'^2*x^2 now considering the particles time independent H'ψ(x) = Eψ(x) the eigenvalues of this Hamiltonian is based on En = (n+ 1/2)ℏω where ground state has non-zero energy. (2) I have no idea how to start this problem. Thank you for your help.