Re: [Phys-l] photoelectric effect & photon emission

[John Denker <jsd@av8n.com>]

On 04/27/2008 06:05 PM, Paul Lulai wrote:
> I have a question regarding photon emission & quantum states. When an
> electron absorbs energy and gets excited, when it transitions to a
> new /n/, does it actually exist in between these n values?  Does it
> dis-appear while it is inbetween these n values?  Does the wave
> function describing it simply change, so it doesn't end up with any
> trouble existing in between n=1 & n=2 (where it should Not be in
> terms of probabilities)?
>
> I have this same question for when the excited electron 'falls' from
> n=2 to n=1.  I understand that the energy is released by screaming
> out a photon.  I do not quite get if the falling electron exists in
> some 1<n<2 state, if the wave function describing the electron has
> changed to cover for this, or what.

To paraphrase Bill Clinton, it depends on what the meaning
of "exists" is.

Fact:  Typically the transition from the N=1 eigenstate to the
N=2 eigenstate (or any other two states) takes some time.
  A) If you don't measure the system during that time, then
   during the transition it "exists" in both states, or 
   neither.  You don't know and you don't care.
  B) If you measure it using operators that measure definite
   N, then you will observe it to be /either/ in N=1 /or/ N=2
   but never both and never anything in between.
  C) However, there are plenty of other measurement operators
   in the world, and you are free to choose to use them.  In
   particular, there are operators that will tell you, essentially
   that the system is halfway between N=1 and N=2.

All this is well developed in the field of magnetic resonance, i.e.
NMR and ESR, and there is a nice terminology for it:  The full 
transition from N=1 to N=2 could be accomplished with a π pulse.
If you can apply a π pulse, then you can just as easily apply
a π/2 pulse, which is guaranteed to take the system _halfway_
from N=1 to N=2.

One commonly encounters the assertion that QM requires the
system to jump from one energy level to another, but this is
98% hogwash.  You can make it true under certain circumstances,
but it's certainly not true in general.