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

By J. J. Sakurai

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43) sincethe eigenvalueof Nu," is one (cf. Eq. 31). 46) lftk,,n,r ftkn,o,, krai 4/ fl4r,ar! o. " t, h k , a , + 1 , . . ) . (2,47) Thus ad,,",has the property of creating an additional photon in state (ku,dr), leaving the occupuation numbers of states other than (kr, dr) unchanged. "is called the creation operator for a photon in state k, a. In contrasr, Ny,o,being diagonal, doesnot changethe occupation number of photons; it simply gives as its eigenvaluethe number of photons in state k, a. we might say that the three operators a[,o, ek,o,and Nu," correspond respectively to the Creator (Brahma), the Destroyer (Siva), and the preserver(Vishnu) in Hindu mythology.

E(d') exp[-i(o - {See,for example,Kittel (1958),pp. 175-176. 158) 48 1( THE QUANTUM THEORY OF RADIATION where we have replaced €'k'xand e ikx by 1, since in the long-wave approximation the atomic electron may be assumed to be situated at the origin. , ,rn' r , a ) . 15e) with a; : lk I c and ar' : lk'l c as usual. Therefore we must treat a double A. The A. p interaction actingattrcan either annihilatethe incident photon (k,a) or create the outgoing photon (k', a'). When the A'p interaction acts again at a time /, which is later than /, it must necessarilycreatethe outgoing photon (k', a') if the outgoing photon has not yet been created.

4) - 0. In other words, the photon spin is either parallel or antiparallel to the propagation direction. We note that the absenceof the zn : 0 state has an invariant meaning only for a particle whose mass is strictly zero. " The description of the polarization state with et as the base vectors is called the circular polarization representation in contrast to the linear polarization representationbased on €(r) and e('). €(T) : l, € ( r ) . €(r) : 0. 73b) 0. (t) in place o f € ( 1 ) a n d e ( 2 ).

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