Riemann Zeros & an Exponential Potential

Abstract

In this paper, a given exponential potential ae^bx on the Real half-line is studied. It is found that it is possible to relate this to the imaginary part of the Riemann zeros. WKB method is also extended to recover the potential from the Eigenvalue Staircase for the Riemann zeros. This eigenvalue staircase includes the oscillatory and smooth part of the number of Riemann zeros. For simplicity, the unit 2m=1= ħ is used in this paper.