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Young operator methods for fermion systems

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Alternative methods to the standard Young technique for the construction of Fermion wave functions in the spin orbital formalism are presented and shown to be equivalent to the standard technique. To develop these methods: (i) the starting or primitive function is factored into spin and spatial parts, (ii) the conjugacy feature required to satisfy the antisymmetry principle is exploited, (iii) the necessary commutation relations with the Fermion antisymmetrizer are shown to hold and (iv) the one-to-one correspondence between the independent picture of the Young tableaux and the independent Slater determinants is used. This last feature has the advantage of reducing all three methods to rapid efficient graphical procedures. Each method is analyzed to consider the amount of labor involved to carry it out. Several examples of the methods are given for constructing both electronic wave functions and spin functions.

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Yu, Y., Palting, P. & Chiu, Y. Young operator methods for fermion systems. Theoret. Chim. Acta 94, 125–141 (1996). https://doi.org/10.1007/BF00191644

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Key words

  • Young operator
  • Conjugacy
  • Wave function