Quantum Mechanics of Harmonic Oscillator in External Fields

A report presents a theoretical study of a harmonic oscillator in homogeneous or nonhomogeneous externally applied electric and/or gravitational fields. The standard quantum-mechanical formalism for a simple harmonic oscillator, starting with the Hamiltonian and the associated creation and annihilation operators, is modified to incorporate the additional terms representing the external fields. The correspondingly modified solutions of the Schroedinger equation are derived.