Understanding Quantization of Energy: Can We Produce EM Waves of Any Energy?

[Cheman]

Quantization of energy...

We say that electrons have set energy levels, and certain energies they cannot possesses whilst in a certain atom. Is it still possible to produce photons / EM waves of any energy we desire? I mean, by looking at the equation E = hf it would appear we can - if we put in any value for f we can get any value for E. (obviously this would mean not being pedantic and talking about -ve numbers, etc. ) We can't just say "yeh we found out a wave with this frequency has this energy - but it doesn't exist!" - can we?

Thanks in advance.

 

[SpaceTiger]

We say that electrons have set energy levels, and certain energies they cannot possesses whilst in a certain atom. Is it still possible to produce photons / EM waves of any energy we desire?

In principle, yes, though there might be practical upper and lower limits.

"yeh we found out a wave with this frequency has this energy - but it doesn't exist!" - can we?

The energy levels of a quantum system are quantized, but in general, the solutions can be perturbed by small amounts so that the energy levels all shift a bit, allowing for the production of a photon of arbitrary energy. Alternatively, you can just exploit the Doppler effect and start moving with respect to the photon or emitting atom. Depending on your velocity, you'll observe a slightly different wavelength for the photon.

 

[masudr]

I think the point is that E=hf is not the be all and end all of describing photons. Instead, we've got

$$\hat{H}\psi=E\psi$$

for a bound system, such as an atom, you'll find that you get discrete values of E, instead of a continuous range.

 

[SpaceTiger]

I think the point is that E=hf is not the be all and end all of describing photons. Instead, we've got

$$\hat{H}\psi=E\psi$$

for a bound system, such as an atom, you'll find that you get discrete values of E, instead of a continuous range.

My point is that this fact doesn't put restrictions on a continuous range of possible photons in the universe, it just restricts them for a given atom/molecule.

 

[masudr]

My point is that this fact doesn't put restrictions on a continuous range of possible photons in the universe, it just restricts them for a given atom/molecule.

Yes of course, although when the orignal poster speaks of "energy levels" he/she almost invariably refers to an atom or molecule, or some other kind of bound system.