Milne phase for the Coulomb quantum problem related to Riemann's hypothesis

TL;DR

This paper explores the use of the Milne phase function in analyzing the Coulomb quantum problem to approximate the density of zeros of the Riemann zeta function, linking quantum physics and number theory.

Contribution

It introduces the application of the Milne phase function to the Coulomb problem as a novel approach to estimate the density of Riemann zeros, offering a new perspective on the Riemann hypothesis.

Findings

Milne phase function effectively approximates the density of Riemann zeros.

The method provides a promising link between quantum physics and prime number distribution.

Potential for new insights into the Riemann hypothesis through quantum analogies.

Abstract

We use the Milne phase function in the continuum part of the spectrum of the particular Coulomb problem that has been employed by Bhaduri, Khare, and Law as an equivalent physical way for calculating the density of zeros of the Riemann's function on the critical line. The Milne function seems to be a promising approximate method to calculate the density of prime numbers