  Nambu mechanics is a generalized Hamiltonian dynamics characterized by an
extended phase space and multiple Hamiltonians. In a previous paper [Prog.
Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical
structure is hidden in Hamiltonian dynamics, that is, the classical time
evolution of variables including redundant degrees of freedom can be formulated
as Nambu mechanics. In the present paper we show that the Nambu mechanical
structure is also hidden in some quantum or semiclassical dynamics, that is, in
some cases the quantum or semiclassical time evolution of expectation values of
quantum mechanical operators, including composite operators, can be formulated
as Nambu mechanics. We present a procedure to find hidden Nambu structures in
quantum/semiclassical systems of one degree of freedom, and give two examples:
the exact quantum dynamics of a harmonic oscillator, and semiclassical wave
packet dynamics. Our formalism can be extended to many-degrees-of-freedom
systems; however, there is a serious difficulty in this case due to
interactions between degrees of freedom. To illustrate our formalism we present
two sets of numerical results on semiclassical dynamics: from a one-dimensional
metastable potential model and a simplified Henon--Heiles model of two
interacting oscillators.
