A very basic question about the the origin of quantum levels

[WarpedWatch]

Does anyone know why quantum states exist? In other words, is there an explanation for why the universe is built from discrete levels vs. some other system? I've scanned over numerous books on quantum mechanics and the history of quantum mechanics but I can never find a layman's answer to this question. A few times people have pulled out equations and tried to "explain" this discrete behavior via mathematics, but it seems to me that the math might be a tautological "explanation" since it seems that the mathematical description followed the experimental observation of natural phenomena.

So is the quantum nature of our universe just something that "it is what it is"? Or is there a deeper explanation of some sort?

I've always pictured the quantum leaps as being the result of some kind of standing wave phenomena, the outcome of probability functions interfering with each other or some such concept, but that was just a wild guess on my part and I've never heard of any deeper explanation.

Can somebody at least provide a hint to me as to why we see things leap like they do?

Thanks.

 

[Chopin]

First off, it's important to understand that not everything in the universe is built out of quantized energy levels. For instance, a free particle traveling through space can have any energy at all. There are no quantized levels--there are a continuum of possible states. So fundamentally, QM does not say that there is some finite number of energy states in the universe, or anything like that.

So if that's the case, why do we spend so much time talking about quantized energy levels? The answer is that sometimes, the energy levels of a particle are indeed quantized, but they become quantized due to the environment we place the particle in. Specifically, when we confine the particle in some sort of potential well, we change its continuous spectrum of energy levels into a discrete one. This happens, as you mentioned, due to standing wave phenomena. The actual details get technical, and involve solving the Schrödinger Equation for the correct boundary conditions of the particle, but the basic idea is that only specific states out of the continuum of possible states are compatible with the constraints we place on the particle, so only those states are possible.

So, because the quantization is an effect of the particle's environment, different environments will lead to different energy levels. For instance, if we place an electron around a single proton, it will take on one of a series of specific energy levels (the emission spectrum of hydrogen.) However, if we place the same electron around two protons that are set up close together, the electron will take on a somewhat different set of energy levels. Actually calculating those energy levels gets tricky, but it's a general principle that any time you put a particle into any sort of confining environment, you'll get some kind of quantized spectrum of energy levels, whose levels are dependent on the exact form of the confinement.

 

[WarpedWatch]

Chopin,

thanks very much for your reply. Knowing that these "chunks" of energy are dependent upon their environment helps clear up some of my confusion. A large part of my confusion stemmed from how the electron shells would "know" where their "steps" would be and how such steps could be fixed in relationship to some sort of "energy space" or whatever it might be called, but knowing that these steps are an artifact of the atomic environment helps me a lot.

Thanks again.

 

[jtbell]

The standing-wave analogy is actually a very good one. You may be aware than in a rectangular-box-shaped room, sound waves have a certain set of resonant frequencies which correspond to standing waves along the three dimensions of the room. In QM, solving the Schrödinger equation for a particle in a rectangular box with "impenetrable" walls gives us very much the same set of standing waves of the QM wave function ψ, with frequencies that give us the allowable energies via Planck's formula E = hf.