Mathematical Physics


A Hamiltonian Whose Energies Are the Zeros of the Riemann XI Function

Authors: Jose Javier Garcia Moreta

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in one dimension 2 2 d V (x) dx - + for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros 2 n n E =g Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to simplify notation. · Keywords: = Riemann Hypothesis, Functional determinant,

Comments: 12 Pages.

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[v7] 2012-11-22 05:57:29

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