Now let us consider a different problem: the quantum harmonic oscillator. Here the potential has the same functional dependence as in the classical case: V(x) = 1/2 * m * omega^2 * x^2

Since in this case the potential is never infinitely large, we do not have strict boundary conditions, which makes a solution via the shooting method much more difficult, as we will explore in the next two lectures.

Below you find a summary of the results that we can also derive analytically (see my other course here on udemy).