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Homework Help: Help help (Helmholtz equation)

  1. May 17, 2006 #1
    dear friends :)

    "Classical and noncllasical symetries for helmholtz equation" help help.:yuck:
     
  2. jcsd
  3. May 17, 2006 #2
    what specific problem are you stuck on? i've just done a module on he Helmholtz equation which i aced. il be happy to help.

    xxxx Gareth
     
  4. May 17, 2006 #3
    By far, the most active area of research linking QM and number theory is the work concerning the 'spectral interpretation' of the Riemann zeta zeros, suggesting a possible approach to the Riemann hypothesis involving quantum chaos.

    We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension n consisting of n2 operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in $\C^n$ which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.

    Some useful notes a friend lent me, and that i never gave back.....

    xxxx Gareth
     
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