How can something have a fraction of a quantum of energy? I thought energy levels had to be discreet integer multiples of Planck's constant? The more I read about Quantum Mechanics, the less I understand!
I think that only applies for particular bounded situations (like electrons). There's nothing inherent in the wave function that says energy is discrete multiples; it's only due to the boundary conditions in the electron (i.e. the energy at r=0 and r=inf IIRC) that forces particular solutions.
The analogy (it's actually quite similar in the differential equations) is a string. If you hold both ends only certain solutions are possible; standing waves where the length of the string is a multiple of half the wavelength. But if you don't, anything is possible.
