Supersymmetric quantum mechanics and the Riemann hypothesis

Abstract

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the vanishing ground state energies in this model. The model provides a natural form of supersymmetry.

5 pages, 1 figure

References in corpus (2)

• Physics of the Riemann Hypothesis
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics

Cited by in corpus (1)

• A symmetry perspective of the Riemann zeros