By J. J. Sakurai

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**Extra info for Advanced Quantum Mechanics Sakurai (1967)**

**Example text**

Rmust satisfy E^ - E, -l ha:0. 118) Spontaneousemission in the dipole approximation. In the case of spontaneous :mission. -rfany incident electromagneticwave. 99) wilh et"t omitted and ny,o set equal to zero. here or satisfies the energy conservation Ea: En * firo. The normalization ',olume Zcancels out as it should. r20) is typically of the order of several thousand angstrom units whereas sincetrphoron rhe atomic radius is of the order of one anqstrom unit. xr)rl2{... r2r) by its leading term 1.

We must somehow incorporate the Pauli exclusion principle. This can be done. In 1928P. Jordan and E. P. Wigner proposed a formalism in which we again consider the operators bl. 50) { A ,B } : A B + B A . The operatorsb| and b, are again interpreted as the creation and annihilation operators, and the index r provides a collective description of the momentum state, the spin state, and according to the Dirac hole theory (to be discussedin Sections 3-9 and 3-10), the sign of the energy as well. 49), we cannot put two particles in the same state.

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. Otherwise we would end up with a zero matrix element. Between t, and t, the atom is in state lwhich is, in general, different from A and B.