2020
DOI: 10.48550/arxiv.2002.12825
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Riemann Hypothesis, Modified Morse Potential and Supersymmetric Quantum Mechanics

Abstract: In this paper we discuss various potentials related to the Riemann zeta function and the Riemann Xi function. These potentials are modified versions of Morse potentials and can also be related to modified forms of the radial harmonic oscillator and modified Coulomb potential. We use supersymmetric quantum mechanics to construct their ground state wave functions and the Fourier transform of the ground state to exhibit the Riemann zeros. This allows us to formulate the Riemann hypothesis in terms of the location… Show more

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Cited by 2 publications
(2 citation statements)
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“…Recently there has been several investigations of the interesting relation of supersymmetric quantum mechanics to the Riemann hypothesis [20] [21] [22] [23]. All three of the functions discussed above can be realized as ground state wave functions in supersymmetric quantum mechanics (SUSY-QM).…”
Section: Relation To Supersymmetric Quantum Mechanicsmentioning
confidence: 99%
“…Recently there has been several investigations of the interesting relation of supersymmetric quantum mechanics to the Riemann hypothesis [20] [21] [22] [23]. All three of the functions discussed above can be realized as ground state wave functions in supersymmetric quantum mechanics (SUSY-QM).…”
Section: Relation To Supersymmetric Quantum Mechanicsmentioning
confidence: 99%
“…In some recent studies, the relationship between the Riemann zeta function and various aspects of physics has been explored [6][7][8][9][10][11]. In another study, the Riemann zeta function relates to scattering amplitudes in quantum field theory [12].…”
mentioning
confidence: 99%