[Phys-l] Atomic energy levels between stable levels

["John SOHL" <jsohl@weber.edu>]

No great surprise, John is absolutely correct. The idea that nothing exists between energy levels is wrong. A better way to think of it is that there are no stable states between the levels, in this case, n=1 and n=2. The atom can certainly exist with intermediate energy, it just cannot stay there. 
 
There is a whole continuous range of energy levels between states. These are known as virtual energy levels. The electron will not "park" there but it can certainly "pause en route" at a virtual energy level. This works best when you have very strong electric fields (i.e., LOTS of photons) such as in a pulsed laser. 
 
For easy numbers lets assume that you have an atom with an energy level at 0 eV (the ground state) and an energy level at 4 eV but no energy level at 2 eV. Normally, you would figure that a 2 eV photon would not be absorbed because there is no resonance between 0 eV and 2 eV in that atom. So, the 2 eV photon zips right on through and nothing happens. Standard QM, everyone is happy.
 
But, with a honking big laser pulse there are enough photons available that the atom can pause at a virtual state and be there long enough for a second photon to push the atom up to the higher state, the 4 eV state in this case. Thus, you can get a transition from 0 eV to 4 eV with no "true" intermediate state and with only 2 eV photons coming in. 
 
This whole field is known as multiphoton spectroscopy. One aspect of this technique is REMPI = Resonantly Enhanced Multi-Photon Ionization. This is a common technique in the field of Rydberg state spectroscopy = the study of highly excited energy levels in atoms and molecules. 
 
Finally, just what is a "honking big" laser pulse? Not that much actually, at least in energy terms. 50 mJ of laser energy will very easily do multiphoton spectroscopy if the pulse is short, say 5 ns or so. Note that the peak power is pretty impressive though since P=E/t we get P = 50mJ/5ns = 10 megawatts of laser power! So, you don't have much energy and it is not on for long, but when it is on you have a LOT of power coming into that atom. So you have on order of 10^17 photons arriving in 5 ns. The result is that improbable transitions become significant => ta da, transitions where no intermediate energy level "exists." 
 
All the best,
 
John
 
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John E. Sohl, Ph.D.
Professor of Physics
Weber State University
2508 University Circle
Ogden, UT 84408-2508

voice: (801) 626-7907, fax: (801) 626-7445 
e-mail: jsohl@weber.edu 
web: http://physics.weber.edu/sohl/ 

> > > John Denker <jsd@av8n.com> 4/27/2008 7:41 PM >>>
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?  

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.