Perturbation of Quantum Harmonic oscillator and its effect on the Quantum Field Theory

TL;DR

This paper investigates how a specific perturbation in a quantum harmonic oscillator influences the creation of coherent states and impacts the quantum field theory of electromagnetic fields, linking observation to field coherence.

Contribution

It introduces a new perturbation that acts as a coherent state generator, connecting observation with photon state coherence in quantum electromagnetic theory.

Findings

Ground state becomes a coherent state of the original oscillator

Perturbation acts as a coherent state generator

Explains the role of observation in photon coherence

Abstract

Here a special case of perturbation in quantum harmonic oscillator is studied. Here we assume the perturbed potential to be a Harmonic Oscillator that has been shifted in the position space.We construct the new creation and annihilation operators for the new Hamiltonian to find out its energy eigenstates. What is interesting about the solution of this system is that we find out that the ground state of this system is a coherent state of the ground state of the original harmonic oscillator. We know that the Hamiltonian of electromagnetic field is similar to that of the harmonic oscillator where the electric field and magnetic field are expressed in terms of time evolution of annihilation and creation operators. According to the quantum electromagnetic field theory, photon states are expressed as the coherent states of the ground states of the unperturbed harmonic oscillator.In the previous research works,it has been established how coherent states provide a better picture of Electric field compared to the energy eigenstates. This paper mainly deals with why the coherent states provide a more complete picture of electric and magnetic field theory compared to just energy eigenstates. Here we find how our perturbation act as a coherent state generator and adds a new term in the Hamiltonian. The Perturbation is thought to arise from the only available interaction i.e. observation. The perturbation also explains how observation leads to coherence of photon states. We will find out how the new perturbation affects the time evolution of electromagnetic field. This also explains how the classical electromagnetic field theory takes into account the factor of observation, due to which the classical laws are in perfect agreement with the quantum laws.