March 5, 1998

PHY 442 - Problem Set # 13

Consider the "coherent" electromagnetic state defined in terms of the number eigenstates by

$$\vert{\cal{E}}\gt \equiv e^{-\frac{1}{2} \vert{\cal{E}}\vert^2} \sum_{n=0}^{\infty} \frac{{\cal{E}}^n}{\sqrt{n!}} \vert n\gt.$$

Evaluate the following expectation values of the Magnetic Field operator ${\bf{B}}$:

1.

$<{\cal{E}}\vert{\bf{B}}\vert{\cal{E}}\gt$.

2.

$<{\cal{E}}\vert{\bf{B}}^2\vert{\cal{E}}\gt$.