Interaction of Radiation and Matter

The time-dependent perturbation changes the system s state function from exp -iE t/hyif to the superposition (9.122). Measurement of the energy then changes to one of the energy eigenfunctions exp -iE i,t/h)il/ i, (reduction of the wave function, Section 7.9). Tie net result is a transition from stationary state n to stationary state m, the probability of such a transition being 

We now consider the interaction of an atom or molecule with electromagnetic radiation. A proper quantum-mechanical approach would treat both the atom and the radiation quantum mechanically, but we shall simplify things by using the classical picture of the light as an electromagnetic wave of oscUlating electric and magnetic fields. 

A detailed investigation, which we omit (see Levine, Molecular Spectroscopy, Section 3.2), shows that usually the interaction between the radiation s magnetic field and the atom s charges is much weaker than the interaction between the radiation s electric field and the charges, so we shall consider only the latter interaction. (In NMR spectroscopy the important interaction is between the magnetic dipole moments of the nuclei and the radiation s magnetic field. We shall not consider this case.) 

As noted at the end of Section 9.9, bm( )P gives the probability of a trausition to state m from state . There are two cases where this probability becomes of significant magnitude. If oi = (o, the denominator of the second fraction in brackets is zero and this fraction s absolute value is large (but not infinite see Problem 9.22). If a = - o, the first fraction has a zero denominator and a large absolute value. 

A defect of our treatment is that it does not predict spontaneous emission, the emission of a photon by a system not exposed to radiation, the system falling to a lower energy level in the process. Quantum field theory does predict spontaneous emission. 

For co = -CO, we get El - E = hv. Exposure to radiation of frequency v has induced a transition from stationary state n to stationary state m, where (since v is positive) eI eI,. The system has gone to a lower energy level, and a qnantum-field-theory treatment shows that a photon of energy hv is emitted in this process. This is stimulated emission of radiation. Stimulated emission occurs in lasers. 

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We assume that the absorbing gas is of a uniform composition and in thermal equilibrium. The absorption coefficient, which is defined by Lambert s law, Eq. 3.1, is expressed in terms of the probabilities of transitions between the stationary states of the supermolecular system, in response to the incident radiation. Assuming the interaction of radiation and matter may be approximated by electric dipole interaction, i.e., assuming the wavelengths of the radiation are large compared with the dimensions of molecular complexes, the transition probability between the initial and... 

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