Why are quantum energy levels discrete in a potential well? What started out as a mathematical trick invented by Max Planck has become an established idea. Energies at the quantum level increase and decrease by integer multiples (n) of fh (frequency times Planck's constant). Let's plot a diagram to see what we can make of it.
The diagram above has a stair-step shape as energy levels go from n = 1 to n = 4. But what happens if we lay it on its side?
Now it looks like some sort of binary, oscillating wave. Let's smooth out the rough edges.
Yes, it most definitely looks like a wave. This is consistent with the fact that quanta are particle-waves. Since particles can behave like waves, it makes perfect sense that changes in energy would behave like waves as well. We measure the energy level when the wave peaks, and no energy is added or subtracted until the next peak.
Update: Below is a possible mathematical formula for the purpose of describing the wave-like character of changing energy levels.
It is the absolute value of a sine wave raised to the power of infinity. This causes all values to be zero or one. When the value is one, n increases or decreases by q; otherwise there is no change in n.
