Let's consider a coherent state for a QHO which we denote as $\psi_{\lambda}(x,t)$.
While one can derive the appropriate expression for the coherent state, what I am interested in is a commentary made about the probability density function that one calculates for when the system finds itself in such a state: $$|\Psi(x; t)|^2 = \frac{1}{\sqrt{\pi} x_0} \exp\left\{-\frac{[x - x_0 \sqrt{2} |\lambda| \cos(\omega t - \phi)]^2}{x_0^2}\right\},$$ where $x_0=\sqrt{\frac{\hbar}{m\omega}}$.
The commentary is the following:
$A=\sqrt 2 x_0|\lambda|$ represents the classical amplitude.
In the limit of large mass $m$, $x_0\rightarrow0$ and the wave-packet (I believe it refers to the above expression which is in fact, from my understanding, a pdf that is expressed as a wave function.) converts to a $\delta$ distribution at $x=A\cos(\omega t-\delta)$. This represents the classical solution.
Can someone explain to me how to obtain this $\delta$-like function from the above-mentioned expression. I fail to understand the derivation.
Is there an intuitive understanding as to why a mass increase will bring us to the classical case?
