Layman question about quantum theory.

[jsicolo]

Hi folks,

I've been watching the Teaching Company videos on quantum mechanics, and I have a few questions regarding energy quantization.

It seems he is saying that energy can only appear in the universe in discrete quantities, which explains blackbody radiation and the heat capacity results.

e=hf explains the relationship between energy and frequency, which implies that if we can only have certain discrete values of energy, we are only allowed to have certain values of f. Is this true, and if so, how do we generate the frequencies that are allowed?

Also, it seems like there must be some minimal energy delta between allowed energy states in order for energy to be quantized. What is this value, and how do we calculate it?

If I'm way off base, please enlighten me! I've been wondering about this stuff for a while.

Thanks,
Jim

 

[vanhees71]

No, it's not true. The energy of a non-interacting particle or photon in free space is continuous. For a particle with a given momentum it's E=h f, where f is the frequency of the corresponding wave mode of the quantum field describing this particle.

 

[krd]

e=hf explains the relationship between energy and frequency, which implies that if we can only have certain discrete values of energy, we are only allowed to have certain values of f. Is this true, and if so, how do we generate the frequencies that are allowed?

You're allowed lots of frequencies - millions of them, billions of them. There are different ways of generating them. Radio waves are the same thing as light waves - and you can create them just by oscillating the voltage in a piece of metal, you're using for your transmitter. Pick your frequency and away you go.

Also, it seems like there must be some minimal energy delta between allowed energy states in order for energy to be quantized. What is this value, and how do we calculate it?

I think I know what's got you confused. Atomic spectral lines. They are limited to discrete frequencies - because they're created by electrons making a jump from one energy level to another - so there's no in between. Electrons can be excited to jump to a higher state, and when they fall back they release a photon of a precise frequency. Energy of a photon is given as E_{energyofphoton} = h_{PlancksConstant}v_{frequencyoflight}

For the Atomic spectral lines it's

E2_{higherenergylevel} - E1_{lowerenergylevel} = E_{energyofphoton} = hv

So if you called the energy levels E1, E2, E3, E4, E5, etc, you're limit to frequencies v1, v2, v3,v4, v5, etc

But something like a tungsten filament light bulb, the emitted light is not restricted to discrete lines. You get all the colours of the rainbow.

 

[Kholdstare]

No, it's not true. The energy of a non-interacting particle or photon in free space is continuous. For a particle with a given momentum it's E=h f, where f is the frequency of the corresponding wave mode of the quantum field describing this particle.

Energy is indeed available in discrete quantities. The fact that the amount of energy that comes with one photon can change depending on frequency, does not mean you can change the photon frequency/energy all by itself.

 

[jsicolo]

Hi guys, thanks for all your answers. I think I've got it now.

Saying that energy is quantized isn't completely correct taken by itself. Saying energy is quantized means it's quantized for a given frequency.

You can have whatever frequency you want, but for that frequency, you will only find energy in lumps of e=hf. For instance, you can't find a packet of green light with e = 1.5h(fgreen) because that would be 1.5 photons.

Does that sound right?

Thanks,
Jim

 

[ZapperZ]

Somehow, I think that this thread has gotten several things crossed and gotten confusing.

The confusing part here is by what is meant as "quantized". I think an analogy is warranted here.

Say that you have a bunch of tennis balls that you are shooting at a target. Each tennis balls has a mass m, and you shoot it with KE of 1/2 mv^2. So far, nothing surprising here.

Now, you shoot at the target a series of these tennis balls. Each one of them carries KE of 1/2 mv^2. When we say "quantized" for light, for example, this is what we meant, that the energy comes in discrete clumps! Each tennis ball brings with it this 1/2 mv^2 amount of energy.

However, in my tennis ball cannon, I can vary the speed of the tennis balls that come out of the cannon. In fact, I can vary it continuously. This means that v can vary continuously, and thus, I can change KE as much or as little as I like. so v isn't "quantized" in this case, even if at each v, the energy arrives at the target in discrete clumps.

The same can be applied to light, depending on the source. At synchrotron light sources, I can have a continuous spectrum of light being produced, because all I need to do is change the spacing in an undulator, by any continuous amount, in principle. So the frequency of that light can be adjusted without any "discreteness". Yet, the light being generated still arrives in "clumps" of photons.

Zz.