Spurious Photon States at the Quantum Harmonic Oscillator with Glauber-Bessel Hamiltonian

Commonly, coherent states can be represented in terms of an exact expansion of Fock's states and a Gaussian distribution. This paper explores the harmonic quantum oscillator through integer-order Bessel functions expected to replace Gaussian profiles. As consequence of having opted Bessel polynomials, the annihilation and creator operators acquire a new mathematical form. This led to construct a kind of Glauber-Bessel Hamiltonian that reproduces standard quantum oscillator energies as well as spurious terms that are interpreted as an inherent noise. In praxis, this novel Hamiltonian can be employed to model cases in which there is evidence of spurious pulses in an experimental scenario of photons correlation without any formalism of perturbation theory.