Decimal orbitals

[questionposter]

So I know that the energies and possible wave mechanics of matter in the universe are quantized, but do things cancel out in the classical world if its not a near perfect vibration? Because if I do experiments where I move water back and forth, if I do it at just the right frequency, I can sustain a wave who's periods perfectly fit within the container the water is waving in, but if I don't do it at just the right frequency, I don't know exactly what happens, do waves crash into each other too soon or not form too late and thus there is no self sustaining wave? Why exactly can't electrons exist at other decimal energies?

[Schrödinger's hat]

Hmm, energy loss and wave speed in a bathtub is too slow for this to make an intuitive model for explaining this. I also don't know how well a classical wave and energy loss translate to bound quantum states, but I'll give it a go.

 

So I'll fall back on my favourite example: A guitar string, or other taught wire.

You can feed energy in at the wrong frequency, but it tends to leak out again.

If you think of plucking a string (or even better is rubbing it with a bow like a violin), what you're inputting is a big mixture of frequencies.

You'll note that when you pluck the guitar string you don't hear white noise coming out again.

This is because the energy of frequencies that aren't harmonics doesn't stay in the string very well. Instead it goes into moving the head of the guitar, or transfers to the body very quickly. You can see how this will be the case if you look at [math] v=f\lambda[/math].

When f is not a harmonic, the wave amplitude cannot be zero at the ends of the string, so it will wind up pulling on the ends where it is attached much more.

One way to hear this is to mute the string with your other hand and pluck it. Then listen carefully while you pluck it normally. You'll notice there's the same sharp plucking sound.

 

As a result of all this, the string (a while after being plucked) will only carry energy in frequencies that are harmonics of the base note.

 

 

Mathematically these harmonics are equivalent to the bound states of our quantum particle.

The other states are the ones that don't fit into the classical analogue very well. I usually think of it as a sum-over-paths thing (very much closer to your thoughts about the waves crashing into each other). Will ponder further.

This could just be what Dr Rocket is always saying, 'Difficult questions have simple, easy to understand, wrong answers'.

[questionposter]

So if you can pluck a string and not play it right, when the universe began, couldn't there have been electrons trying to vibrate at decimal energies that just couldn't sustain their existence due to this destructive interference?

[Schrödinger's hat]

So if you can pluck a string and not play it right, when the universe began, couldn't there have been electrons trying to vibrate at decimal energies that just couldn't sustain their existence due to this destructive interference?

 

More that the probability would 'leak' out of the bound state (like energy leaks out of the string) and you'd find the electron somewhere else, such as in a free state (which does not have a discrete energy spectrum).

It might then emit a photon and become bound again.

[DrRocket]

So I know that the energies and possible wave mechanics of matter in the universe are quantized, but do things cancel out in the classical world if its not a near perfect vibration? Because if I do experiments where I move water back and forth, if I do it at just the right frequency, I can sustain a wave who's periods perfectly fit within the container the water is waving in, but if I don't do it at just the right frequency, I don't know exactly what happens, do waves crash into each other too soon or not form too late and thus there is no self sustaining wave? Why exactly can't electrons exist at other decimal energies?

 

 

You have just discovered resonance.

 

Now go read a introductory book on ordinary differential equations. Pay special attention to second order equations with constant coefficients.

 

You might also want to watch this video.

[questionposter]

You have just discovered resonance.

 

Now go read a introductory book on ordinary differential equations. Pay special attention to second order equations with constant coefficients.

 

You might also want to watch this video.

 

I'm familiar with resonance already, but I just don't get exactly how it works in the atomic world.

 

Also, I know that steel and concrete are actually kind of flexible depending on their percent compositions, but how the hell does it do that? Did that Tesla death vibrator finally work?

Edited December 13, 2011 by questionposter

[Schrödinger's hat]

I'm familiar with resonance already, but I just don't get exactly how it works in the atomic world.

 

Also, I know that steel and concrete are actually kind of flexible depending on their percent compositions, but how the hell does it do that? Did that Tesla death vibrator finally work?

 

No death vibrator. Just a breeze -- and a strong resonance. Energy kept getting fed in, but didn't leave.

[DrRocket]

I'm familiar with resonance already, but I just don't get exactly how it works in the atomic world.

 

 

In the atomic world resonances are realized as eigenfunctions of the Hamiltonian.