Mark W Coffey 2006 J. Phys. A: Math. Gen. 39 877 doi:10.1088/0305-4470/39/4/009
Mark W Coffey
Show affiliationsQuantum 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.
03.65.Ge Solutions of wave equations: bound states
02.10.Ox Combinatorics; graph theory
81Txx Quantum field theory; related classical field theories (See also 70Sxx)
81Qxx General mathematical topics and methods in quantum theory
Issue 4 (27 January 2006)
Received 17 August 2005, in final form 28 November 2005
Published 11 January 2006
Mark W Coffey 2006 J. Phys. A: Math. Gen. 39 877
In-Ha Sung et al 2003 J. Phys. D: Appl. Phys. 36 939
Robert J Young et al 2006 New J. Phys. 8 29
G Cao et al 2004 New J. Phys. 6 159
Christos Siopis et al. 2009 ApJ 693 946
Louis H Kauffman and Samuel J Lomonaco Jr 2002 New J. Phys. 4 73
T Schroeder et al 2008 New J. Phys. 10 113004
T K Koponen et al 2008 New J. Phys. 10 045014
V. Cvetkovic and Z. Tesanovic 2009 EPL 85 37002
K W D Ledingham et al 2003 J. Phys. D: Appl. Phys. 36 L79