The solutions of the generalized classical and quantum harmonic oscillators with time dependent mass, frequency, two-photon parameter and external force: The squeezing effects

Singh, Shailendra Kumar; Mandal, Satya

doi:10.1016/j.optcom.2010.07.009

Cited by 11 publications

(8 citation statements)

References 37 publications

(59 reference statements)

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“…In order to acomplish this, we use Eqs. (9) and (11) and infer that the general structure of the transformed Floquet operator…”

Section: The Lie Algebraic Approachmentioning

confidence: 98%

“…In many applications as radio-frequency ion traps [1][2][3][4][5][6][7][8], quantum optics [9][10][11][12], cosmology [13,14], quantum field theory [15], quantum dissipation [16][17][18][19][20][21][22], magneto transport in lateral heterostructures [23][24][25][26] and even gravitational waves [27] the time evolution of particles in quadratic potentials is frequently examined. The one-dimensional, generalized time-dependent quadratic Hamiltonian is given bŷ H = a 1 (t) + a 2 (t)x + a 3 (t)p + a 4 (t)x 2 + a 5 (t)p 2 + a 6 (t) (xp +px) ,…”

Section: Introductionmentioning

confidence: 99%

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Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

Sandoval-Santana

Ibarra-Sierra

Cardoso

et al. 2016

Journal of Mathematical Physics

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We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.2

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“…In order to acomplish this, we use Eqs. (9) and (11) and infer that the general structure of the transformed Floquet operator…”

Section: The Lie Algebraic Approachmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

Sandoval-Santana

Ibarra-Sierra

Cardoso

et al. 2016

Journal of Mathematical Physics

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“…Some of its most widespread applications are the atomic and molecular bonds that, under certain approximations, can be modelled by quadratic potentials. Time-dependent general harmonic oscillators (GHO), the most general version of a simple quantum harmonic oscillator, are not only relevant from the theoretical point of view but are also at the heart of many interesting applications as quantum optics [1,2,3], radio-frequency ion traps [4,5,6,7,8,9,10,11], Email address: akb@correo.azc.uam.mx ( A. Kunold 2 ) quantum field theory [12], quantum dissipation (Kanai-Caldirola Hamiltonians) [13,14,15,16,17,18,19], and even cosmology [20,21].…”

Section: Introductionmentioning

confidence: 99%

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

et al. 2015

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“…In effect, t m ( ) stands for effective mass that varies with time. Recently, molecular systems and other dynamical systems with time-dependent effective mass, as well as position-dependent effective mass, became a topic of research [7,37,40,[52][53][54][55][56][57][58][59][60]. In some cases, effective mass of a molecule in a system may vary through its interaction with the environment or various excitations such as energy, temperature, stress, pressure, phonon, etc.…”

Section: Hamiltonian and Invariantmentioning

confidence: 99%

Quantum features of molecular interactions associated with time-dependent non-central potentials

2017

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The research for quantum features of molecular Coulomb interactions subjected to a time-dependent non-central potential has many applications. The wave functions of this system can be obtained by using an invariant operator, which is necessary for investigating a time-dependent Hamiltonian system. Regarding time dependence of the system, one can confirm that the formula of this operator is in general somewhat complicated. Hence, in order to solve its eigenvalue equation, special mathematical techniques beyond separation of variables method, such as the unitary transformation method, the Nikiforov-Uvarov method, and the asymptotic iteration method, should be employed. The double ring-shaped generalized non-central potential of which evolution explicitly depends on time is introduced as a particular case. The complete quantum solutions of the system can be identified from the eigenstates of the invariant operator. These solutions are useful for analyzing dynamical properties of the system.

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The solutions of the generalized classical and quantum harmonic oscillators with time dependent mass, frequency, two-photon parameter and external force: The squeezing effects

Cited by 11 publications

References 37 publications

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

Quantum features of molecular interactions associated with time-dependent non-central potentials

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