Shirokov has proposed the unified formalism for quantum and classical mechanics [@Shirokov1979d]–a reformulation of both the theories in terms of the same physical and mathematical concepts. Crudely speaking, this formalism is based on the well-known fact that observables of quantum mechanics can be converted from operators to functions (i.e., to a very similar form as in classical physics) by means of the Weyl representation [@Weyl1950]. In these terms, the probability density of quantum states is represented by the Wigner quasiprobability density distribution function [@Wigner1932]. Hence, in order to construct a classical ensemble that corresponds to the quantum particle, we shall calculate the Wigner function $W(P_R, P_{\rho}; R, \rho)$ for the initial condition (\[InitialCondition\]), $$\begin{aligned}
\label{WingerFunctionForInitialState}
&& W(P_R, P_{\rho}; R, \rho) = (2\pi)^2 \int \Psi\left( R-R'/2, \rho-\rho'/2\right)\\
&& \qquad\quad \times \Psi^*\left( R+R'/2, \rho+\rho'/2\right) e^{i\left( P_R R'\ + P_{\rho} \rho' \right)} d\rho' dR', \nonumber\end{aligned}$$ where $\Psi (R, \rho) \equiv \Psi_N(\alpha; 0, R, \rho)$. Since $\phi_g(\rho)$ has no zeros and decays exponentially at infinity, we shall approximate it by a Gaussian $$\begin{aligned}
\label{GaussApproxGroundState}
\phi_g(\rho) \propto \exp\left[ -\rho^2 / \left(2\sigma_{\rho}^2\right) \right],\end{aligned}$$ where we set $\sigma_{\rho} = 1.5$ (a.u.). Substituting Eqs. (\[GaussApproxGroundState\]) and (\[InitialCondition\]) into Eq. (\[WingerFunctionForInitialState\]), one readily obtains $$\begin{aligned}
W(P_R, P_{\rho}; R, \rho)  