Advanced Quantum Mechanics by Professor Dr. Franz Schwabl (auth.) PDF

By Professor Dr. Franz Schwabl (auth.)

ISBN-10: 3662054183

ISBN-13: 9783662054185

ISBN-10: 3662054205

ISBN-13: 9783662054208

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Namaizawa, and M. Voss, Phys. Rev. B13, 1360 (1976); L. A. Maradudin, Phys. Rev. C. Grimes, and G. Adams, Phys. Rev. Lett. 15) since (1)01 aka(O)aL(O) 11>0) = -nka + l. 16) as can be immediately seen from the field equation. From this it follows that On the right-hand side there now appears not only Gka(t), but also a higherorder correlation function. In a systematic treatment we could derive an equation of motion for this, too. 18)

One can think of it as being included in the previous formulas as part of the spatial degree of freedom x. If the spin is to be given explicitly, then one has to make the replacements ~(x) --+ ~u(x) and a p --+ a pu and, in addition, introduce the sum over a, the z component of the spin. 11) . p,U 8 The hat on the operator, as used here for nq and previously for the occupationnumber operator, will only be retained where it is needed to avoid confusion. 28 1. 12) the corresponding form applying in the momentum representation.

Ni -1, ... ). I ... ,ni,"') = = (1-ni)(-1)2LJ<,nJ(ni+1)1 .. · ,ni,"') (1 - ni) I.. 13a) a;ail .. · ,ni,"') =ni(-1)2LJ<,nJ(1-ni+1)1··· ,ni,"') == ni I· . ,ni,' .. 13b) , since for ni E {O, I} we have = ni and (_1)2LJ<' nj = l. 13b) one can regard a; ai as the occupation-number operator for the state Ii). 13a,b), one obtains the anticommutator In the anticommutator [ai, a}l+ with i is different: =1= j, the phase factor of the two terms Likewise, [ai, aj 1+ for i =1= j, also has different phase factors in the two summands and, since aiai I...

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Advanced Quantum Mechanics by Professor Dr. Franz Schwabl (auth.)


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