G$.$ Consider the following states $||>$ and $||>$

$||e^{-\frac{|{|}^2}{2}}{\displaystyle \underset{n=0}{\overset{}{}}}\frac{{}^n}{\sqrt[\phantom{2}]{n!}}|{}_n|>,$ and $,||e^{-\frac{|{|}^2}{2}}{\displaystyle \underset{n=0}{\overset{}{}}}\frac{{}^n}{\sqrt[\phantom{2}]{n!}}|{}_n|>$

where $,$ are complex constants.

Consider the operator

hat

Compute the trace of hat$(Q)$ and find its explicit expression in terms of $,.$ What is the trace in the limit $?$ Is it what you expected?