Advanced Quantum Mechanics - download pdf or read online

By Professor Dr. Franz Schwabl (auth.)

ISBN-10: 366203929X

ISBN-13: 9783662039298

ISBN-10: 3662039311

ISBN-13: 9783662039311

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Sample text

This is arbitrary but, once chosen, must be adhered to. 7) The effect of the operator a! must be a! I... , ni,"') = (1 - ni)( _l)L:;<;n; I··. ,ni + 1, ... ). 8) The number of particles is increased by 1, but for astate that is already occupied, the factor (1- ni) yields zero. The phase factor corresponds to the number of anticommutations necessary to bring the a! to the position i. The adjoint relation reads: (... , ni, ... 1ai = (1 - ni)( -l)L: i <; n; ( ... , ni + 1, ... 1. 9) This yields the matrix element (...

Particles with opposite spin are not affected by the Pauli principle. nq". nq". (x-x)). 8) and the abbreviation x = kF Ix - x'l, we finally obtain 9 . (x - x') = 1 - 6"(smx - xcosx)2 . 0 2. - .. -7r---~ 47r- kF lx - x I I Fig. 4. The pair distribution function 9CT<7(X - x') . 16) plotted in Fig. 4. If a fermion is removed at x, the particle density in the vicinity of this point is strongly reduced. In other words, the probability of finding two fermions with the same spin at separations ;S k F1 is smalI.

In the spirit of the Ritz variational principle, the single-particle wave funetions IPi(X) are now determined so as to minimize the expeetation value of H. As subsidiary eonditions, one must take aeeount of the normalizations J ICPil 2d3x = 1; this leads to the additional terms -ci(J d3xlcpi(X) 12 -1) with Lagrange parameters Ci. 2a-e). Taking the variational derivative with respeet to cP; yields: ( - : : V7 2 Z;2) CPi(X) + t, Jd3x'Ix ~2 x'llcpj(x')1 cpi(X) 2 - N -L Dm,; m,; )=1 J 2 d3x' Ix ~ x'l cP; (X')cpi (x') .

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

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