Thanks for your comments. E_0 is the ground state energy (lowest energy) of the system. In my solution, I introduced dimensionless quantities, so for example the mass is set to m = 1, the reduced Planck constant is also set to \hbar = 1. Thus energies calculated are normalized and expressed in terms of the ground state energy. If you are familiar with the harmonic oscillator, you would remember that the quantized energy levels for a harmonic oscillator can be expressed as E_0, 3E_0, 5E_0, 7E_0, etc.
I hope this helps.