Quantal Cumulant Mechanics as Extended Ehrenfest Theorem

Equivalent Hamiltonian approach to quantum cosmology of integrable models

“…Note that κ 2,0 κ 0,2 = 1/4 is the minimal value which comes from the uncertainty principle (i.e., we assume a coherent state initially). Note also that κ 2,0 κ 0,2 −κ 2 1,1 is a constant [32,33]. In Fig.…”

“…Since we know that p ≈ y − y 0 evolves linearly in time in the classical system, we illustrate evolutions of variables as functions of p. Note that κ 2,0 κ 0,2 = 1/4 is the minimal value which comes from the uncertainty principle (i.e., we assume a coherent state initially). Note also that κ 2,0 κ 0,2 −κ 2 1,1 is a constant [32,33]. In Fig.…”

“…It is well-known that the Ehrenfest's theorem tells Recently, Shigeta et al [32,33] defined an expression for the expectation value by means of cumulants among the canonical pair of the variables q and p. That is defined as…”

“…Then, the following simultaneous equations are derived from the Ehrenfest's theorem: [32,33] q =H (0,1) , (4.5) p = −H (1,0) , (4.6) κ 2,0 = 2κ 2,0H (1,1) + 2κ 1,1H (0,2) , (4.7)…”

“…Then, the following simultaneous equations are derived from the Ehrenfest's theorem: [32,33] q = H(0,1) , (4.5)…”