By J. J. Sakurai

ISBN-10: 0201067102

ISBN-13: 9780201067101

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**Example text**

It is also called Rayleigh scattering becausethis problem was treated classicallyby Lord Rayleigh.

88) wherewe have suppressed the subscriptsk, a. 88) is satisfied whenever Nd - +N : i. This leads to a new uncertaintyrelation for the corresponding observables: aNAd = 1. 8e) For example, if the phase difference of two plane-wave components is given precisely,then we cannot tell the occupation number associatedwith each of the wave components. The above uncertainty relation can be used to derive a more familiarJooking uncertainty relation for the light beam. Since the momentum operator is written as the sum of the number operators weighted by ftk (cf.

Vao, h__ -i ( t r l1 e i k ' x ' p , . 79). Note that the annihilation operator for a photon with momentum and polarization different from hk arrd e(") gives a zero matrix element. It is instructive to compare this expressionwith the expressionwe obtain using the semiclassicaltheory of radiation in which the vector potential A is treated classically. e7) - ,4ffir*'. e8) A(abs) - [[abs)"tt< will do, where According to the semiclassicaltheory the absorption probability is proportional 'z to the intensity I Ao | ; in the quantum theory it is proportional to nu,o. __

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

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