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An obstruction for q-deformation of the convolution product

Hans van Leeuwen and Hans Maassen

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We consider two independent q-Gaussian random variables and and a function chosen in such a way that and have the same distribution. For we find that at least the fourth moments of and are different. We conclude that no q-deformed convolution product, parallelling the known cases q = 0 and q = 1, can exist.


PACS

02.30.Tb Operator theory

02.50.-r Probability theory, stochastic processes, and statistics

03.65.Ge Solutions of wave equations: bound states

MSC

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

60Exx Distribution theory (See also 62Exx, 62Hxx)

Subjects

Mathematical physics

Computational physics

Quantum information and quantum mechanics

Dates

Issue 15 (7 August 1996)

Received 15 January 1996



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