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- W2779218468 abstract "The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and discuss the eigenvalues of the results. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, the Hilbert-Pólya conjecture is discussed, and it is heuristically shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2." @default.
- W2779218468 created "2018-01-05" @default.
- W2779218468 creator A5077382435 @default.
- W2779218468 date "2017-01-01" @default.
- W2779218468 modified "2023-09-23" @default.
- W2779218468 title "A Schrödinger equation for solving the Bender-Brody-Müller conjecture" @default.
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- W2779218468 doi "https://doi.org/10.1063/1.5012170" @default.
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