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Invariants for Time-Dependent Harmonic Oscillators from the Real Representation of Solution

100%
Liang M., Zhang Z., Yuan B.
Acta Physica Polonica A
|
2004
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vol. 105
|
issue 3
253-262
EN
The invariants for the time-dependent one-dimensional harmonic oscillator and the time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived from the real representation of the exact solution to the equation of motion. Mathematically, the orthogonal functions invariant is the angular momentum of an isotropic time-dependent two-dimensional harmonic oscillator. Based on the invariants obtained here, the wave function for time-dependent two-dimensional harmonic oscillator in a static magnetic field in cylindrical coordinate is simply derived and the dynamical and geometrical phases are easily got by expressing the wave function as the superpositions of the wave functions of time-dependent two-dimensional harmonic oscillator in rectangular coordinate. For the driven system, the driving induced dynamical phase and the geometrical phase are respectively associated with the classical Hamiltonian and de Broglie wave of the center motion of the wave function.
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The Method of Jacobi Last Multiplier for Integrating Nonholonomic Systems

80%
Zhang Y.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
443-446
EN
In this paper, a new integral method of nonholonomic dynamical systems is put forward. The differential equations of motion of nonholonomic systems in phase space are established. The definition of the Jacobi last multiplier of the systems is given, and the relation between the Jacobi last multiplier and the first integrals of the systems is discussed. The researches show that the solution of the systems can be found by the last multiplier if the quantity of first integrals of the systems is sufficient. An example is given to illustrate the application of the results.
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Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

70%
Baleanu D.
Open Physics
|
2006
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vol. 4
|
issue 4
503-510
EN
The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed.
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