Figure 4

Time evolution of (a) the probability amplitude to find the resonator in the position x \(\vert \psi (x) \vert ^{2}\), (b) expectation value for the position, \(\langle x(t) \rangle\) in blue, and momentum, \(\langle p(t) \rangle\) in red, with solid lines and squares for analytic and numeric results, in that order; we show standard deviations, \(\sigma _{x}(t)\) and \(\sigma _{p}(t)\), as shaded regions or error bars for analytic and numeric results, and (c) Heisenberg uncertainty relation, \(\sigma _{x}(t) \sigma _{p}(t)\), for an initial state provided by the ground state of the standard harmonic oscillator in a Caldirola–Kanai QHO with \(\gamma = - \omega / 4\).