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

By J. J. Sakurai

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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. This is just what is neededif the electronsare to satisfythe Pauli exclusionprinciple.

We wish to conclude this section with a derivation of Planck's radiation 1aw from the point of view of quantum field theory. rst) ^hdtk, - e-rAkt where lu*'. "pt r l A ) 1 , ) . e(o)stk'xtl (B le-ik'*,6t"' S)* -

A \mF)e;fnF-"" (P'-e("')ut(p'el"''-)r'r) x l E , r e ' " ' . ", l p ' eh:o" ' 1 " ' 1 \ - z' -. r o/ r . l El-E11ha' / ll ' . t To obtain the differential cross section we must divide this transition probability by the flux density which is just clV, since initially there is one photon in the normalization box of volume V. e , do " / . i ) l E , ^ € , o , . | ) ' . 1 ( p . r62) where ru standsfor the classicalradius of the electron,and ,,--#=hh- 2 . 8 x2 l o - 1 3 c m . 162) was flrst obtained by H.

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