The states $|\alpha,m>$, defined as ${ a^{ \dagger}}^{ m}|\alpha>$ up to a normalization constant and $m$ is a nonnegative integer, are shown to be the eigenstates of $f(\hat{ n},m)\hat{ a}$ where $f(\hat{ n},m)$ is a nonlinear function of the number operator $\hat{ n}$. The explicit form of $f(\hat{ n},m)$ is constructed. The eigenstates of this operator for negative values of $m$ are introduced. The properties of these states are discussed and compared with those of the state $|\alpha,m >$.
Categories: quant-ph