# Quantum Theory of Interaction of Radiation Field with Matter

## Abstract

In this chapter we show that the electromagnetic field can be considered as an infinite set of harmonic oscillators, each corresponding to a particular value of the frequency, wave vector, and a particular state of polarization. Comparing with the quantum mechanical treatment of harmonic oscillators, we replace the generalized coordinates and generalized momenta by operators. By imposing the commutation relations between the canonical variables, it is shown that the energy of each oscillator can increase or decrease by integral multiples of a certain quantum of energy; this quantum of energy is known as the *photon*. Having quantized the field, we show that the state which corresponds to a given number of photons (also referred to as the number state) for a particular mode does *not* correspond to the classical plane wave. Indeed, we show that the eigenstates of the annihilation operator (which are known as the *coherent states*) resemble the classical plane wave for large intensities.

## Keywords

Harmonic Oscillator Coherent State Radiation Field Beam Splitter Spontaneous Emission## References

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