Figure 1

Evolution of the SU(1,1) coherent state parameter $\xi \left(t\right)=x\left(t\right)+iy\left(t\right)$ given in Eqs. (16, 17). The initial conditions $\mathbf{\left(}x\left(0\right),y\left(0\right)\mathbf{\right)}$ are (a) (0.1,0), (b) (0.3,0), (c) (0.5,0), and (d) (0.99,0). We used $\omega =1$ and $\lambda =1$.Reuse & Permissions

Figure 2

(Color online) Variances $V\left(q\right)$ and $V\left(p\right)$ given in Eqs. (22, 23), respectively, and UP. (a)–(d) are connected with the numerical values of the SU(1,1) coherent state parameter $\xi \left(t\right)=x\left(t\right)+iy\left(t\right)$ depicted in Figs. 1a, 1b, 1c, 1d. Thus, the initial conditions $\mathbf{\left(}x\left(0\right),y\left(0\right)\mathbf{\right)}$ of (a)–(d) are the same as those of Figs. 1a, 1b, 1c, 1d in turn. The straight horizontal reference line is ${\hslash }^2/4$ which is minimally allowed UP for the harmonic oscillator. (${\mathrm{d}}^{\prime }$) is a highly enlarged graph of the lower part of (d) (but only for UP), displayed on the purpose of checking distinctly whether the uncertainty principle also holds for the case of (d). We used $m=1$, $\hslash =1$, $k=1/4$, $\omega =1$, and $\lambda =1$.Reuse & Permissions

Figure 3

(Color online) Evolution of the SU(1,1) coherent state when disappearing the damping force, i.e., $\lambda =0$, with the initial condition $\mathbf{\left(}x\left(0\right),y\left(0\right)\mathbf{\right)}=\left(0.3,0\right)$. (a) Plot of the SU(1,1) coherent state parameter $\xi \left(t\right)=x\left(t\right)+iy\left(t\right)$. (b) Variances $V\left(q\right)$ and $V\left(p\right)$. (c) Expectation value of the quantum energy $E_k$. The straight horizontal reference line exhibited in (b) is ${\hslash }^2/4$. We used $m=1$, $\hslash =1$, $k=1/4$, and $\omega =1$.Reuse & Permissions