Physics/Electron Energies in an Atom
Iím trying to understand the distinction between an electrons energy state, its actual energy and the statement that Ďan electron can have several different energies at the same timeí. Iím currently reading The Quantum Universe by Brian Cox and Geoff Forshaw (p106) and I think (but Iím not at all sure) that the several energies are Ďprobabilities that an electron can have different energiesí but does this mean that it could be at its ground state (n=1 Ė 90% probability) or have be at a higher energy state (n > 1 Ė 10% probability). Iím confused because I thought an electron could only be in one energy state at a time with the state changing via the emission or absorption of a photon. To understand this Iíve tried drawing a set of probability sine wave with energy on the x-axis and probability on the y-axis but in the end I just donít understand the theory. Iím not a physics student Ė just interested Ė but in the end Iíd like to understand perhaps a few simple examples of how electron energies are calculated. Any help will be much appreciated.
> Iím confused because I thought an electron could only be in one energy state at a time
Welcome to the confusing world of quantum mechanics!
The problem you are running into is that, in QM, it is meaningless to say an electron IS in one energy state, as opposed to another, UNLESS you take a measurement. PRIOR to the taking of a measurement, the electron IS in ANY and ALL energy states that are not forbidden.
It is NOT the case that we lack the ability to perceive the energy state of an electron, or that the electron "knows" its state but we don't. The energy state of an electron is FUNDAMENTALLY unknowable UNTIL we take a measurement.
If we detect a photon coming from an atom, that's a measurement -- THEN we know what energy state the electron started in, and which one it went to. But, PRIOR to the detecting the photon, the electron IS in ANY state, and in EVERY state.
What we are reduced to saying is, "We know that, given these conditions, there is this probability of an electron being in this state, and this probability of it going to this other state. Thus, the fraction of electrons in the entire system that will go between the first state and the second is this number."
This is not unlike statistical thermodynamics, where we say that the probability of a molecule at a certain velocity or vibrational state is a specific number. But we do that because we realize that the effort of working out the velocity of EVERY molecule is just too daunting, and will yield no useful information. But in QM, the problem of working out the energy state of even ONE electron isn't just too daunting, it's FUNDAMENTALLY IMPOSSIBLE.
Confusing? Yes! Einstein found this idea so repugnant that he rejected it -- but he was wrong!