By J. J. Sakurai
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Additional info for Advanced Quantum Mechanics Sakurai (1967)
4d,a nhyr - -S- V -AEnr I _j' (2,rs7) This is Planck's famous law which opened up the twentieth-centuryphysicsof the quantum domain. f They are both based on thermal equilibrium between the atoms and the radiation field. 153) which is an automatic consequenceof the hermiticity of the Hamiltonian used in the quantum theory of radiation. Note also that in our derivation we do not distinguish between the contributions from spontaneousemission and induced emission. Although our attention has been focused in this section on the radiative transitions between two atomic states,the techniqueswe have acquired can readily be applied to a host of other phenomena.
Physically this selection rule is a consequence of the fact that one unit of angular momentum is carried away by the spin of the emitted photon in an El transition. r2e) where fI and flr, u stand for the parity operator and its eigenvalue. 122)can also be written as waa- e2a3 , cos2 dA, @(") iifu3lxr,12 where we have defined the angle @(") by c o s@ ( o )- l x r r . € ( o ) l / l* r , l . 13r) tThose who are unfamiliar with the Wigner-Eckhart theorem and Clebsch-Gordan coefficientsmay consult Merzbacher(1961),Chapter 22; Messiah (19621,Chapter 13.
T) : l, € ( r ) . €(r) : 0. 73b) 0. (t) in place o f € ( 1 ) a n d e ( 2 ). 74) to the vacuum state. Conversely,ai," l0> with a : 1,2 and k in the z-direction can be regardedas a 50/50 mixture of the m: 1 and m : -L sIate. To sum up, the quantum postulate applied to the canonical variables of the radiation oscillator naturally leads to the idea that the quantum-mechanical excitations of the radiation field can be regarded as particles of mass zero and spin one. It is a general feature of the quantum theory of fields that with every field we associate a particle of definite mqss and spin.
Advanced Quantum Mechanics Sakurai (1967) by J. J. Sakurai