New PDF release: Advanced Quantum Mechanics Sakurai (1967)

By J. J. Sakurai

ISBN-10: 0201067102

ISBN-13: 9780201067101

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Additional resources for Advanced Quantum Mechanics Sakurai (1967)

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.

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


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