bei48482_FM

The selection rule requiring that lchange by 1 if an atom is to radiate means that

an emitted photon carries off the angular momentum equal to the difference

between the angular momenta of the atom’s initial and final states. The classical ana-

log of a photon with angular momentum is a left or right circularly polarized elec-

tromagnetic wave, so this notion is not unique with quantum theory.

Quantum Theory of the Hydrogen Atom 221

Quantum Electrodynamics

T

he preceding analysis of radiative transitions in an atom is based on a mixture of classical

and quantum concepts. As we have seen, the expectation value of the position of an atomic

electron oscillates at the frequency of Eq. (6.33) while passing from an initial eigenstate to

another one of lower energy. Classically such an oscillating charge gives rise to electromagnetic

waves of the same frequency , and indeed the observed radiation has this frequency. However,

classical concepts are not always reliable guides to atomic processes, and a deeper treatment is

required. Such a treatment, called quantum electrodynamics,shows that the radiation emitted

during a transition from state mto state nis in the form of a single photon.

In addition, quantum electrodynamics provides an explanation for the mechanism that causes

the “spontaneous” transition of an atom from one energy state to a lower one. All electric and

Excitation

energy, eV

13.6

10

5

0 n = 1

n = 2

n = 3

n = 4

n = ∞

l = 0 l = 1 l = 2 l = 3

Figure 6.13Energy-level diagram for hydrogen showing transitions allowed by the selection rule

l 1. In this diagram the vertical axis represents excitation energy above the ground state.

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