Invariants and the evolution of coherent states for a charged particle in a time-dependent magnetic field

Malkin, I.A.; Man’ko, Vladimir I.; Trifonov, D. A.

doi:10.1016/0375-9601(69)90740-3

Cited by 87 publications

(116 citation statements)

References 2 publications

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“…In the coordinate representation the wave functions take the form of an exponential of a quadratic 27 (for the reader's convenience in this formula we restore the dimensions x = q h/m 0 ω 0 , m 0 being a mass parameter)…”

Section: The Canonical Squeezed States As L D and U Coherent Statesmentioning

confidence: 99%

“…For r = n in inequality (27) we have the extension of the Robertson relation to the case of several states…”

Section: Characteristic Uncertainty Re-lations and Their State Extensmentioning

confidence: 99%

“…We note that extended relations (27) and (28) are invariant under the nondegenerate linear transformations of the operators X 1 , . .…”

Section: Characteristic Uncertainty Re-lations and Their State Extensmentioning

confidence: 99%

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Generalized uncertainty relations and coherent and squeezed states

Trifonov

2000

J. Opt. Soc. Am. A

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Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of the canonical coherent states. The standard SU(1,1) coherent states are shown to be the unique states that minimize the Schrödinger uncertainty relation for every pair of the three generators and the Robertson relation for the three generators. The characteristic uncertainty inequalities are naturally extended to the case of several states. It is shown that these inequalities can be written in the equivalent complementary form.OSIC codes: 270.6570, 270.0270.

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Section: The Canonical Squeezed States As L D and U Coherent Statesmentioning

confidence: 99%

“…For r = n in inequality (27) we have the extension of the Robertson relation to the case of several states…”

Section: Characteristic Uncertainty Re-lations and Their State Extensmentioning

confidence: 99%

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Generalized uncertainty relations and coherent and squeezed states

Trifonov

2000

J. Opt. Soc. Am. A

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“…Indeed this relation known as Schrödinger-Robertson uncertainty inequality [5] can be minimized and gives rise to new sets of coherent and squeezed states ( see the pioneering works [6][7][8]). The states resulting from this minimization have different names in the literature such as correlated states [6][7][8] or Robertson intelligent states [9]. More recently, there has been much interest in such states for Lie algebras [9][10][11][12][13] as well as for quantum systems evolving in various potentials [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Analytic representations based on su(3) coherent states and Robertson intelligent states

Daoud

2004

Journal of Mathematical Physics

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“…To this aim we make an efficient use of the method of time-dependent quantum invariants [16,17,18]. We construct a four complex parameters (z, u, v, w) family of states |z, u, v, w; κ, t of general SO, which diagonalize the general complex combination of the three linearly independent Hermitian invariants I j (t).…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for the general nonstationary oscillator with a singular perturbation

Trifonov¹

1999

J. Phys. A: Math. Gen.

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Three linearly independent Hermitian invariants for the nonstationary generalized singular oscillator (SO) are constructed and their complex linear combination is diagonalized. The constructed family of eigenstates contains as subsets all previously obtained solutions for the SO and includes all Robertson and Schrödinger intelligent states for the three invariants. It is shown that the constructed analogues of the SU (1, 1) group-related coherent states for the SO minimize the Robertson and Schrödinger uncertainty relations for the three invariants and for every pair of them simultaneously. The squeezing properties of the new states are briefly discussed.

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Invariants and the evolution of coherent states for a charged particle in a time-dependent magnetic field

Cited by 87 publications

References 2 publications

Generalized uncertainty relations and coherent and squeezed states

Generalized uncertainty relations and coherent and squeezed states

Analytic representations based on su(3) coherent states and Robertson intelligent states

Exact solutions for the general nonstationary oscillator with a singular perturbation

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