The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function

Details The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function

2006-11-13

arxiv.org/abs/quant-ph/0611134v1

Physics

Quantum Physics

19 pages, 3 figures

Scientific paper

I have made an ample study of one dimensional quantum oscillators, ranging from logarithmic to exponential potentials. I have found that the eigenvalues of the hamiltonian of the oscillator with the limiting (approachissimo) harmonic potential (~ p(x)2) maps the zeros of the Riemann function height up in the Riemann line. This is the potential created by the field of J(x) that is the Riemann generator of the prime number counting function, p(x), that in turn can be defined by an integral transformation of the Riemann zeta function. This plays the role of the spring strength of the quantum limiting harmonic oscillator. The number theory meaning of this result is that the roots height up of the zeta function are the eigenvalues of a Hamiltonian whose potential is the number of primes squared up to a given x. Therefore this may prove the never published Hilbert-Polya conjecture. The conjecture is true but does not imply the truth of the Riemann hypothesis. We can have complex conjugated zeros off the Riemman line and map them with another hermitic operator and a general expression is given for that. The zeros off the line affect the fluctuation of the eigenvalues but not their mean values.

Affiliated with

Also associated with

No associations

Rating

The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-669796