Fock State - Vacuum Fluctuations

Vacuum Fluctuations

The vacuum state or is the state of lowest energy and the expectation values of and vanish in this state:

The electrical and magnetic fields and the vector potential have the mode expansion of the same general form:

Thus it is easy to see that the expectation values of these field operators vanishes in the vacuum state:

However, it can be shown that the expectation values of the square of these field operators is non-zero. Thus there are fluctuations in the field about the zero ensemble average. These vacuum fluctuations are responsible for many interesting phenomenon including the Lamb shift in quantum optics.

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