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2.3: System of identical fermions and bosons

  • Page ID
    10794
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    The Hilbert space ¡bxif,,' (3.33) for a system of r¿ identical fermions each with spin s and nr identica.l bosons e¿rch with spin .s' is the direct product of the n-ferrnion and zt-boson Hilbert 28 spaces. Thar is, ¡å*i.i,,=t*;ø¿*;i (3.34) /'*;,,';,, ¡ spanned by vecrors of the form (3.35) where I rr{rr¡rr2 ..} > ir the Slate¡ dererminant (3.7) and I ntþl.,ntr...l > is the symmetric determinant (3.23).


    2.3: System of identical fermions and bosons is shared under a not declared license and was authored, remixed, and/or curated by Malcolm McMillian.

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