# Quantization of cavity modes

# Quantization of cavity modes

This chapter begins with a normal-mode analysis of the classical electromagnetic field in an ideal cavity. The resulting expression for the electromagnetic energy has the same form as the energy of a collection of harmonic oscillators, called radiation oscillators. This analogy is the basis for a quantization conjecture in which the classical mode amplitudes are replaced by photon creation and annihilation operators, obeying a version of the canonical commutation relations of quantum mechanics. Fock space is constructed by repeated application of creation operators to the vacuum state. Pure and mixed quantum states of light are described, respectively, by Fock-space vectors satisfying the Schrödinger equation, and density operators satisfying the quantum Liouville equation. The notions of normal ordering and vacuum fluctuations are introduced, and the latter is used to explain the Casimir effect.

*Keywords:*
radiation oscillator, creation/annihilation operator, commutation relation, Fock space, quantum states, density operator, quantum Liouville equation, normal ordering, vacuum fluctuations, Casimir effect

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