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Here a special case of perturbation in quantum harmonic oscillator isstudied. Here we assume the perturbed potential to be a Harmonic Oscillatorthat has been shifted in the position space.We construct the new creation andannihilation operators for the new Hamiltonian to find out its energyeigenstates. What is interesting about the solution of this system is that wefind out that the ground state of this system is a coherent state of the groundstate of the original harmonic oscillator. We know that the Hamiltonian ofelectromagnetic field is similar to that of the harmonic oscillator where theelectric field and magnetic field are expressed in terms of time evolution ofannihilation and creation operators. According to the quantum electromagneticfield theory, photon states are expressed as the coherent states of the groundstates of the unperturbed harmonic oscillator.In the previous research works,ithas been established how coherent states provide a better picture of Electricfield compared to the energy eigenstates. This paper mainly deals with why thecoherent states provide a more complete picture of electric and magnetic fieldtheory compared to just energy eigenstates. Here we find how our perturbationact as a coherent state generator and adds a new term in the Hamiltonian. ThePerturbation is thought to arise from the only available interaction i.e.observation. The perturbation also explains how observation leads to coherenceof photon states. We will find out how the new perturbation affects the timeevolution of electromagnetic field. This also explains how the classicalelectromagnetic field theory takes into account the factor of observation, dueto which the classical laws are in perfect agreement with the quantum laws.

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