1. The problem statement, all variables and given/known data I need to find the energies of the lowest level of the following hamiltonian H = p^2/2m + (mw^2r^2)/2 + L.S (spin 1/2 particle of mass m) The tridimensional harmonic oscilator with a coupling term 2. Relevant equations The first two terms are solved, my question is about the term L.S, which l correspond to the lowest energy? l=0 or l= 1? First, I thought that it should be l=0, but in my class they stated l=1, is it related to the heisenberg principle? 3. The attempt at a solution If the hamiltonian was the free particle with just the term L.S i think l = 0 would follow to a fundamental state of 0 energy and it is wrong (i think)...could you help me please?