## 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.

**Download:** **PDF**

### 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

**Unique-IP document downloads:** 1594 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*