Can Zeta ζ(½+it) be interpreted as a Wave function?

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SUMMARY

The discussion centers on the interpretation of the Zeta function ζ(½+it) as a wave function in quantum mechanics (QM) to explore potential connections to the Riemann Hypothesis (RH). A new approach suggests that the wave curves of ζ(½+it) could describe atomic nuclei, with eigenvalues corresponding to the nontrivial zeros of the Zeta function. While this interpretation introduces a complex version of the Parity Operator, the consensus is that RH, being a mathematical statement, cannot be proven through physics alone. The thread emphasizes that any proof must rely strictly on mathematical methods.

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  • Understanding of the Riemann Hypothesis (RH)
  • Familiarity with the Zeta function and its properties
  • Knowledge of quantum mechanics and wave functions
  • Concepts of Hermitian operators in physics
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  • Research the mathematical properties of the Zeta function and its nontrivial zeros
  • Study the role of Hermitian operators in quantum mechanics
  • Explore existing connections between quantum mechanics and number theory
  • Investigate previous attempts to prove the Riemann Hypothesis
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Mathematicians, physicists, and researchers interested in the intersection of quantum mechanics and number theory, particularly those exploring the Riemann Hypothesis.

Jason C
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In a recent article by BBM in Physical Review Letters highlights another approach to link QM to Zeta to Prove R.H. There approach proved unsuccessful. I want to ask professional Physicists if the following new approach have merit in connecting the Zeta function to QM? This new line of attack is interpreting the wave graph of ζ(½+it) of Zeta as a wave function. Those wave curves in the graph of ζ(½+it) could be describing the atomic nuclei the Eigenvalue(nontrivial zeros) are related to. It is a new Complex version of the Parity Operator and it is Hermitian. It's eigenvalues can mirror the nontrivial zeros of Zeta. Could this wave function interpretation of ζ(½+it) be the new approach in proving Riemann Hypothesis using Physics? The jpeg attachments are visual representations of this new line of attack for proving RH.
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RH is a mathematical statement, so it can be proved (or disproved) only by mathematics. Physics cannot prove RH. Perhaps a proof may be based on some mathematical tool, such as a Hermitian operator, which has applications in physics, but still the proof of RH cannot depend on physics.
 
In any case, PhysicsForums is not the place to discuss personal work. Please read the forum rules.

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