On a Hidden Symmetry of Quantum Harmonic Oscillators

Lopez, Raquel M.; Suslov, Sergeĭ K.; Vega-Guzmán, José

doi:10.48550/arxiv.1112.2586

Cited by 4 publications

(18 citation statements)

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“…This quantum state can be thought of as a special case of a 'nonclassical' oscillator solution originally found by Marhic [116]. The latter has been recently derived in a unified approach to generalized harmonic oscillators (see, for example, [27], [29], [98], [105], [153] and the references therein). These solutions can be verified by a direct substitution with the aid of Mathematica computer algebra system [91] (see also [92]), [105], and [106].…”

Section: The Minimum-uncertainty Squeezed Statesmentioning

confidence: 85%

“…The latter has been recently derived in a unified approach to generalized harmonic oscillators (see, for example, [27], [29], [98], [105], [153] and the references therein). These solutions can be verified by a direct substitution with the aid of Mathematica computer algebra system [91] (see also [92]), [105], and [106]. (In retrospect, the simplest special case β 0 = ±1 and α 0 = γ 0 = δ 0 = ε 0 = κ 0 = 0 is the ground oscillator state [55], [64], [96], [119], [143], [144].…”

Section: The Minimum-uncertainty Squeezed Statesmentioning

confidence: 99%

“…The purpose of this paper is to construct the minimum-uncertainty squeezed states for quantum harmonic oscillators, which are important in these applications, in the most simple closed form. Our approach reveals the quantum numbers/integrals of motion of the squeezed states in terms of solution of certain Ermakov-type system [104], [105]. The corresponding generalizations of Fock states, which were originally found in [116] and recently rediscovered in [105], are discussed in detail.…”

Section: An Introductionmentioning

confidence: 99%

“…Our approach reveals the quantum numbers/integrals of motion of the squeezed states in terms of solution of certain Ermakov-type system [104], [105]. The corresponding generalizations of Fock states, which were originally found in [116] and recently rediscovered in [105], are discussed in detail. As a result, the probability amplitudes of these nonclassical states of motion are explicitly evaluated in terms of hypergeometric functions.…”

Section: An Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The minimum-uncertainty squeezed states for atoms and photons in a cavity

Kryuchkov

Suslov

Vega-Guzmán

2013

J. Phys. B: At. Mol. Opt. Phys.

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We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

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Section: The Minimum-uncertainty Squeezed Statesmentioning

confidence: 85%

Section: The Minimum-uncertainty Squeezed Statesmentioning

confidence: 99%

Section: An Introductionmentioning

confidence: 99%

Section: An Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The minimum-uncertainty squeezed states for atoms and photons in a cavity

Kryuchkov

Suslov

Vega-Guzmán

2013

J. Phys. B: At. Mol. Opt. Phys.

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show abstract

“…where a dot denotes differentiation with respect to t. 5 We have done coordinate transformations and reparametrization from the original expressions in Ref. [18].…”

Section: Time-dependent Wave Function On the Whole Line: A Reviewmentioning

confidence: 99%

Exact time-dependent states for throat quantized toroidal AdS black holes

Maeda

Kunstatter

2017

Phys. Rev. D

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We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and Mäkelä for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.

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Unitary evolution of the quantum Universe with a Brown–Kuchař dust

Maeda¹

2015

Class. Quantum Grav.

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We study the time evolution of a wave function for the spatially flat FriedmannLemaître-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchař dust as a matter field in order to introduce a "clock" in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the universe obeys the classical time evolution in the late time but its variance diverges.

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On a Hidden Symmetry of Quantum Harmonic Oscillators

Cited by 4 publications

References 0 publications

The minimum-uncertainty squeezed states for atoms and photons in a cavity

The minimum-uncertainty squeezed states for atoms and photons in a cavity

Exact time-dependent states for throat quantized toroidal AdS black holes

Unitary evolution of the quantum Universe with a Brown–Kuchař dust

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