## 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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### Submission history

[v1] 5 Jul 2010

[v2] 27 Jul 2010

[v3] 3 Aug 2010

[v4] 18 Nov 2010

[v5] 10 Mar 2011

[v6] 5 Apr 2011

[v7] 2 May 2011

[v8] 28 Jun 2011

[v9] 4 Oct 2011

[vA] 3 Nov 2011

[vB] 13 Nov 2011

[vC] 28 Nov 2011

[vD] 2011-12-04 07:54:17

[vE] 2011-12-14 13:56:54

[vF] 2012-01-25 05:58:47

[vG] 2012-03-26 15:02:21

[vH] 2012-10-06 04:12:18

[vI] 2012-03-26 15:13:42

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

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