[ron123456 (OP)]

Hello....I require the Quantum Jump explanation for the generation of a light wave.....If the electron can exist simultaneously in both energy levels (quantum mechanically) and would only fall in one direction, then how can a sine wave be produced? Classically, it has to radiate as an antenna to produce a sine wave, indicating classically at least, that the electron must spiral around the nucleus of the atom as it descends to radiate an electric field sine wave...Thx for the patience.....

[Halc]

Hello....I require the Quantum Jump explanation for the generation of a light wave.....If the electron can exist simultaneously in both energy levels (quantum mechanically) and would only fall in one direction, then how can a sine wave be produced?

I think it's a mistake to equate a photon to a sine wave. Light has some wave like properties, but is no more a wave than it is a particle.

Classically, it has to radiate as an antenna to produce a sine wave

If you insist on a classic analogy, a one-shot disturbance to water (the moving of a wall at one end of a wavetank) creases a wave on the water, which propagates as a sine wave despite the lack of reciprocating motion. The reciprocating motion is only needed to sustain the wave over time like a radio broadcast, which is hardly the case with a single energy state change.

indicating classically at least, that the electron must spiral around the nucleus of the atom

The classic image of electrons spiraling around the nucleus like little solar systems has been discredited as it seems to cause more confusion than clarification. Quantum particles, unmeasured, do not have classic locations and paths. They only have measurement events.

[evan_au]

Perhaps one way of looking at photon generation is:
- The electron is initially in a higher-energy orbital
- The electron ends up in a lower-energy orbital
- The difference in energy has to go somewhere, which is into a photon
- The energy of the photon is proportional to its frequency by the equation E=hf
- Where E is the Energy
- f is the frequency
- h is Plank's constant

It is only when you have something like a laser, with many in-phase photons that you can say that the electric and magnetic field intensity follows a sine-wave pattern.

See: https://en.wikipedia.org/wiki/Photon_energy

[alancalverd]

If the pattern were other than sinusoidal, I think we would find harmonics in single-transition atomic spectra and Maxwellian propagation would lead to frequency dispersion. Whatever is going on, a sinusoidal model does give the right answer!

[Eternal Student]

Hello....I require the Quantum Jump explanation for the generation of a light wave.....If the electron can exist simultaneously in both energy levels (quantum mechanically) and would only fall in one direction, then how can a sine wave be produced? Classically, it has to radiate as an antenna to produce a sine wave, indicating classically at least, that the electron must spiral around the nucleus of the atom as it descends to radiate an electric field sine wave..

   Hi Ron.
I'm not entirely sure which thing is worrying you.  Is it that there can be a superposition of states?
   If the QM wavefunction shows the electron existing in this superposition of states (some probability to be at the higher energy level + some probability for the lower energy level) then the associated photon also exists in a superposition of states.   There either being a photon or not being a photon.

   In QM you don't need to have any continuous process where the photon (a wave packet in the e-m fields) was being manufactured, like the process you describe where the electron spiraled around the nucleus.  It is either all there or none of it is there.  At no time could you identify when there was half a wave packet or the wave packet was halfway through being manufactured. 

   This doesn't tell you "how" the wave packet is created but we can suggest what it is not like.  It is not like a smooth acceleration of a charged particle and determined just with classical electrodynamics.

[wolfekeeper]

Hello....I require the Quantum Jump explanation for the generation of a light wave.....If the electron can exist simultaneously in both energy levels (quantum mechanically) and would only fall in one direction, then how can a sine wave be produced? Classically, it has to radiate as an antenna to produce a sine wave, indicating classically at least, that the electron must spiral around the nucleus of the atom as it descends to radiate an electric field sine wave...Thx for the patience.....

Why, that's just your basic Quantum Electrodynamics!

https://en.wikipedia.org/wiki/Quantum_electrodynamics

Simples! (Not very, Feynman and co. got the Nobel Prize for it.)

[evan_au]

If the pattern were other than sinusoidal, I think we would find (photon) harmonics...

Photon emission is a quantum process.
- Heisenberg's Uncertainty Principle applies, so there is a tradeoff between uncertainty in energy and uncertainty in position (which you can translate to an uncertainty in time).
- Because a photon is massless, it has a potentially indefinitely lifetime
- So you could take a very long time/very large volume to measure its energy to high precision
- Presumably the same applies to the lifetime of orbitals: if transitions are rare, the lifetime is long, and the energy is very tightly constrained.

PS: Ignoring things like:
-  there are a range of Doppler shifts in a hot gas emitting photons...
- As gas pressure increases, the Pauli exclusion principle leads to broader lines...
- In a magnetic field, you can get doubling of lines, etc etc

[alancalverd]

All true, but if a nonsinusoidal model of a single photon had predictive value we'd find spectral lines at integer multiples of ν for every transition.

That would imply either that E ≠ hv or that h is not constant, because those harmonic lines would be carrying energy.

So a pure sinusoidal (classical) model is the only one that is consistent with quantum mechanics.