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Chinese Phys. B Vol. 19, No. 1, pp. 010306(1-5). Choi, J. R. (2010b). Interpreting quantum states of electromagnetic ﬁeld in time-dependent linear media. Phys. Rev. A, Vol. 82, No. 5, pp. 055803(1-4). Choi, J. R. (2011). An approach to dark energy problem through linear invariants. Chinese. Phys. C, Vol. 35, No. 3, pp. 233-242. Choi, J. R. & Yeon, K. H. (2005). Quantum properties of light in linear media with time-dependent parameters by Lewis-Riesenfeld invariant operator method. Int. J. Mod. Phys.

Therefore, it is possible to obtain zero-point eigenstate q|φ0 (t) of Kˆ from aˆ q|φ0 (t) = 0 and nth order eigenstate by operating aˆ † n times into q|φ0 (t) . Thus we ﬁnally get q|φn (t) = 4 1 Ω √ Hn 2ρ2 (t)h¯ π 2n n! × exp − 1 2ρ(t)h¯ Ω q 2ρ2 (t)h¯ Ω − i 0 eΛ(t) ρ˙ (t) q2 , 2ρ(t) (32) where Hn is nth order Hermite polynomial. For the time-dependent Hamiltonian systems in cases like this, the Schrödinger solutions are different from the eigenstates q|φn (t) by only time-dependent phase factors (Lewis & Riesenfeld, 1969): q|ψn (t) = q|φn (t) exp [iθn (t)].

5. of interference fringe is a major factor that determine the shape of interference in probability density displayed in Fig. 4 (and Figs. 6 and 7 for the superposed squeezed state). Recall that the interference pattern in probability density for an arbitrary superposition state is connected with its WDF via Eqs. (38) and (39). If we consider, in the context of classical mechanics, that the physical attributes of a system exist objectively even when it is unknown, classical mechanics fails to give a reasonable explanation for the negative values in the superposition states.