Help help (Helmholtz equation)

1. May 17, 2006

mathrock79

dear friends :)

"Classical and noncllasical symetries for helmholtz equation" help help.:yuck:

2. May 17, 2006

acceler8

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

3. May 17, 2006

acceler8

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