Download PDF by Professor Dr. Walter Greiner, Professor Dr. Joachim A.: Nuclear Models

By Professor Dr. Walter Greiner, Professor Dr. Joachim A. Maruhn (auth.)

ISBN-10: 3540780467

ISBN-13: 9783540780465

ISBN-10: 3642609708

ISBN-13: 9783642609701

This reprint has been licensed by means of Springer-Verlag on the market in Africa, Middle/South the United States, Israel, Jordan, Lebanon, Saudia-Arabia, Syria, South-East-Asia and China only

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Quantum mechanics insists that the information about which particle occupies which wave function is meaningless because of the indistinguishability of the particles: therefore, a better formalism should not explicitly contain this information. The only meaningful information is how many particles populate each state 'ljJi(r). Calling this the occupation number ni, we can define the many-particle state as an abstract (normalized) vector in the occupation-number representation. 5) The space of these abstract vectors characterized by varying particle numbers is called Fock space.

Solution. According to the triangular rule, the coupling of the vectors is that of two tensors of unit angular momentum to a resulting angular momentum K = 0, I, 2. The general formula is T~ = L(lIKlq Q-q Q)aqbQ _ q (I) q involving the spherical components of the vectors. For K qO) = -(-I)q/V3 to get Tg = =- = ° we can use (llOlq - -fi(aobo - a1b_ 1 - a_1b 1) -fi [azbz + 4(a = - v1(ax bx + iay)(bx - iby) + 4(ax + ayby + azbz ) = - -fia . b x - iay)(bx + iby)] (2) 31 32 2. , the not very surprising result that the scalar built up from the two vectors is just the scalar produCt, aside from a constant factor.

Clearly dealing with such wave functions directly is cumbersome, to say the least. However, it is also clear that there is a lot of superfluous information in these expressions. Quantum mechanics insists that the information about which particle occupies which wave function is meaningless because of the indistinguishability of the particles: therefore, a better formalism should not explicitly contain this information. The only meaningful information is how many particles populate each state 'ljJi(r).

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Nuclear Models by Professor Dr. Walter Greiner, Professor Dr. Joachim A. Maruhn (auth.)


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