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Standard Basis and Ladder operators

  1. Jan 26, 2007 #1


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    Cohen-Tanoudji defines a "standard basis" of the state space as an orthonormal basis {|k,j,m>} composed of eigenvectors common to J² and J_z such that the action of J_± on the basis vectors is given by

    [tex]J_{\pm}|k,j,m>=\hbar\sqrt{j(j+1)-m(m\pm 1)}|k,j,m\pm 1>[/tex]

    But isn't is automatic that such are the effects of the ladder operators as soon as {|k,j,m>} is an orthonormal basis of simultaneous eigenvectors of J² and J_z???

    At least this is the distinct impression I got out of the text preceeding this definition.
  2. jcsd
  3. Jan 27, 2007 #2


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    Yes, C-Tannoudji is a little inaccurate. A standard basis in the irreducible space is a a basis formed by eigenvectors of L_{z} and L^{2}. Period.
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