Advanced Quantum Mechanics Sakurai (1967) by J. J. Sakurai

By J. J. Sakurai

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Jeanswrote an expressi{bn for the energy distribution of the radiation field as a function of o in an ideal situation where the radiation field is enclosedby perfectly absorbing walls. The expressionthey obtained was in satisfactory agreement with observation for low values of or at sufficiently high temperatures,but in marked disagreementfor high values of or. This difficulty led M. He proposedthat: The energy of each radiation oscillator is not an arbitrary quantity but must be an integral multiple of hco,where h is a new fundamental constant in nature.

A is a differentialoperator thatactsoneverything that stands to the right; however, because of the transversality condition V. A : 0, it is legitimate to replacep,. A by A' p,. [V x A(x,r)]*:,,. e5) As we saw in the previous section, A(x, t) is a linear combination of the creation and annihilation operators for photons. The question of which particular creation or annihilation operator gives rise to a nonvanishing matrix element depends entirely on the nature ofthe initial and final statesin question.

It should be clear that, for intense radiation, taking one photon away from the radiation field or adding one photon to it does not make much practical difference. On the other hand, for weak or no incident radiation the classicaldescription runs into difficulty becausethe change in the radiation field brought about by the emission and absorption of a photon by an atom is quite noticeable. 100) quantum fWe recall that the total time-dependent potential that appears in nonrelativistic mechanics must be Hermitian.

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