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Properties and possibilities of quantum shapelets

Mark W Coffey

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Quantum shapelets arise as the solution of a d-dimensional harmonic oscillator or D-dimensional Coulomb problem and may be obtained by requiring scale-space invariance. These functions have application to image processing in conventional or quantum contexts. We recall the scale-space-based derivation of shapelets and present novel properties of these functions, including integral relations, infinite series and finite convolution sums. Many of these relations also have application to the combinatorics of zero-dimensional quantum field theory.


PACS

03.65.Ge Solutions of wave equations: bound states

02.10.Ox Combinatorics; graph theory

02.10.De Algebraic structures and number theory

02.30.Rz Integral equations

03.70.+k Theory of quantized fields

MSC

81Txx Quantum field theory; related classical field theories (See also 70Sxx)

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (See also 42C05 for general orthogonal polynomials and functions)

81Qxx General mathematical topics and methods in quantum theory

Subjects

Mathematical physics

Particle physics and field theory

Quantum information and quantum mechanics

Dates

Issue 4 (27 January 2006)

Received 17 August 2005, in final form 28 November 2005

Published 11 January 2006



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