 Okay, so let's put some pieces together and use our harmonic oscillator model, the potential energy for a harmonic oscillator, and insert that in the Schrodinger equation and begin to solve the quantum mechanical problem. So we know the Schrodinger equation in a couple different forms, a couple different ways of looking at the same equation. Hamiltonian acts on a wave function to give us back an energy times the same wave function that Hamiltonian always has the form minus h squared over 8 pi squared mass, mass for a diatomic molecule is the reduced mass, times a second derivative, that's our kinetic energy term, add to that the potential energy multiplying the wave function and that should equal energy times the wave function if that function in fact solves Schrodinger's equation. So for us in particular, talking about the harmonic oscillator, our potential energy has the form one-half kx squared, so I'll just rewrite that one more time, so our potential energy looks like one-half kx squared multiplying a wave function. So here's the version of Schrodinger's equation for the harmonic oscillator, I've used the harmonic oscillator potential energy one-half kx squared, notice that the function that we're solving Schrodinger's equation for is a function of x, it's a one-dimensional function, so each of these wave functions is just psi of x and Schrodinger's equation is telling us we're looking for a function that if we take these derivatives, these constants times the second derivative, add it to a quadratic function multiplying the wave function, I should get back the original function. So that's the differential equation that we need to solve, that one has a different character than the ones we solved before because of this x squared and the potential energy. So that's the next task we have to solve and we'll do that in a separate video lecture, but let me encourage you before you get to that next video lecture to ask yourself, what would that function look like, what types of functions are there that if we take their second derivatives, add it to x squared times the function, some things cancel when we get back the original function. For example, if you want some things to try, we've seen before that sine of x or sine of constants times x, that seemed to be good at solving the rigid rotor in the particle in a box function. So is that what our wave function should look like? Alternatively, maybe the wave function looks like some polynomial, so let's go ahead and say sine of a times x or a times, I don't know, x cubed or x to the fourth times a different constant. So maybe psi is a polynomial, it's just got x to the fourth, x cubed, x squared, some polynomial involving powers of x, that's another typical option for what a function might look like. You can consider exponential functions, e to the ax, so some function of this type is going to end up being useful to Solve Schrodinger's equation. And I encourage you, before you move on to the next video, go ahead and take some second derivatives, add them to x squared times these functions, or at least do as much of that math as you need to to decide whether this will or won't solve Schrodinger's equation. Whether this will or won't solve Schrodinger's equation, whether this one will or won't solve Schrodinger's equation with the harmonic oscillator potential energy. So after you've done that, I'll see you in the next video lecture where we'll explore what these solutions do in fact look like.