TITLE:
Quantum Light and Coherent States in Conducting Media
AUTHORS:
I. A. Pedrosa
KEYWORDS:
Light, Schrödinger Equation, Invariant Method, Fock States, Coherent and Squeezed States
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.11,
November
25,
2020
ABSTRACT: We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.