Goldbach conjecture sequences in quantum mechanics

TL;DR

This paper explores a novel connection between the Goldbach conjecture sequences and quantum harmonic oscillator states, proposing methods to generate and analyze these sequences through quantum expectation values.

Contribution

It introduces a framework linking Goldbach conjecture sequences to quantum states, including algorithms for deriving GCS from normalized Fock states and analyzing their properties.

Findings

Sequences equivalent to GCS can be derived from normalized quantum states.

States related to GCS are connected to eigenstates of the quantum harmonic oscillator.

The approach addresses degeneracy and mappings between GCS and Goldbach partitions.

Abstract

We show that there is a correspondence between Goldbach conjecture sequences (GCS) and expectation values of the number operator in Fock states. We demonstrate that depending on the normalization or not of Fock state superpositions, we have sequences that are equivalent and sequences that are not equivalent to GCS. We propose an algorithm where sequences equivalent to GCS can be derived in terms of expectation values with normalized states. Defining states whose projections generate GCS, we relate this problem to eigenstates of quantum harmonic oscillator and discuss Fock states directly associated to GCS, taking into account the hamiltonian spectrum and quantum vacuum fluctuations. Finally, we address the problems of degeneracy, maps associating GCS and Goldbach partitions.