Simplified 3B covers
the second third of Volume 3 of The Feynman Lectures on
topics we explore include:
Exchange Model of Forces
Penetration in Particle Exchange
Operators & Matrices
- 2-State &
Splitting & Spin-Spin Interactions
- Electrons in
Crystals & Semiconductors
- Symmetry &
Ionized Hydrogen Molecule
We consider here a
hydrogen molecule that has been ionized by the removal of one electron,
leaving two protons to share the lone remaining electron. Let’s examine
how this electron can be shared.
Two simple basis states present
themselves: the electron could surround the left proton; or it could
surround the right proton. These two states are symmetric and both
effectively result in a neutral hydrogen atom with a lone proton
nearby, as shown in Figure 13-1.
energy required to remove an electron from a neutral hydrogen atom is
13.6 eV. On the atomic scale, 13.6 eV is substantial, about 6 times the
energy of visible light.
For the electron of an ionized hydrogen molecule to jump between states
|1> and |2> it would have to overcome the binding energy of one
proton before falling into the potential well of the other proton. This
is a bit like a golf ball spontaneously disappearing from one cup and
reappearing in another. No golfer has ever seen this happen, because in
classical physics such actions are impossible.
However, as we discovered in Chapter 9, barrier penetration does occur
in the realm of quantum mechanics. Hence there is a non-zero amplitude
H12 for the transition from |2> to |1>. Since 13.6 eV presents a
large barrier, the amplitude H12 is small. By symmetry, states |1>
and |2> must have the same energy (H11=H22) and the same amplitude
to transition from one to the other (H12=H21).