Time-dependent Constants Of Motion Research Articles

Nonstationary linear spin systems in the probability representation

The probability representation of angular momentum states and the connection of the representation with the formalism of the star-product quantization procedure are reviewed. The Schrodinger equation of a general time-dependent Hamiltonian, linear in angular momentum operators, and the evolution equation for the density operator in the probability representation are solved analytically by means of the formalism of linear time-dependent constants of motion. These analytical solutions define wavefunctions and tomograms of states (generic Dicke states), which contain the atomic coherent states as a particular case. The statistical properties of these new states are also evaluated. General forms of analytically solvable Hamiltonians are established in terms of the Euler angle parametrization of the three-dimensional rotations.

Ambiguities Appearing in the Study of Time-Dependent Constants of Motion for the One-Dimensional Harmonic Oscillator

A family of time-dependent constants of motionfor the one-dimensional harmonic oscillator is derived.The relation between constants of motion, Lagrangian,and Hamiltonian is described. A well-defined time-dependent Lagrangian (for whichEuler–Lagrange equations and Legendretransformation are fully satisfied) is not uniquelydetermined.

Generalized Hamiltonian structures for systems in three dimensions with a rescalable constant of motion

The generalized Hamiltonian structures of several three-dimensional dynamical systems of interest in physical applications are considered. In general, Hamiltonians exist only for systems that possess at least one time-independent constant of motion. Systems with only time-dependent constants of motion may sometimes be rescaled and their constant of motion made time-independent. When this is possible, the transformed system may be cast in a generalized Hamiltonian formalism with non-canonical structure functions.