The solution for the Schrödinger equation for a particle in a box, e.g. an electron, is a standing wave with the length $\lambda/2*n$ with $n$ as the number of the orbit or the so called state. Furthermore $n$ is called the principal quantum number.
This standing wave moves up and down with its amplitude but the knots of the standing wave do not move. Now imagine to take these waves and their discrete lengths and wrap them around a circle. What you get, in the opinion of my university professor, is the following:
If I got it right, an electron in a box, considering the Schrödinger equation, has the same matter wave as an electron on an atom orbit. So it moves in the same way if you hit the standing wave.
But I have to say, I do not know how that should work. Why should the particle in the box and the particle on the orbit act identically? And as you can see, there are twice as many half-periods of the wave for each $n$ in the second picture along the orbit as calculated before.