The allowed energy levels for the harmonic oscillator are determined by numerical integration of the Schrodinger equation, starting in the classically forbidden region to the left of the potential. The criterion that the energy is an eigenvalue for the problem is that the wave function decays to zero in the classically forbidden region to the right of the potential. The zero point energy is determined for different values of k. The results are graphed to obtain a functional relationship between the zero point energy and k.
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