Coherent States and Transition Probabilities in a Time-Dependent Electromagnetic Field

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

doi:10.1103/physrevd.2.1371

Cited by 202 publications

(217 citation statements)

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“…In the final stage of publication of the present paper Prof. Dodonov has brought to our attention the very interesting papers, [19], [20], where among other things exact invariants in the form of generalized creation and annihilation operators for a general N-dimensional harmonic oscillator were constructed.…”

Section: Discussionmentioning

confidence: 99%

Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field

Fiore

Gouba

2011

Journal of Mathematical Physics

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We consider an isotropic two dimensional harmonic oscillator with arbitrarily timedependent mass M (t) and frequency Ω(t) in an arbitrarily time-dependent magnetic field B(t). We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) L, I in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors ϕ λ of L, I. We then determine time-dependent phases α λ (t) such that the ψ λ (t) = e iα λ ϕ λ are solutions of the time-dependent Schrödinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent M, B, which is obtained from the above just by setting Ω(t) ≡ 0. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.

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Section: Discussionmentioning

confidence: 99%

Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field

Fiore

Gouba

2011

Journal of Mathematical Physics

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“…where the 2N-vector B(t) is the integral of motion linear in the annihilation and creation operators found in [1], [9] and [18]. This ansatz follows from the statement that the density operator of the Hamiltonian system is the integral of motion, and its matrix elements in any basis must depend on appropriate integrals of motion.…”

Section: Q(b T) = Q(b(t) T = 0)mentioning

confidence: 99%

“…where time-dependent arguments are linear integrals of motion of the quadratic system found in [1], [9] and [18]. The same ansatz is used for the Q-function.…”

Section: Wigner and Q-functionsmentioning

confidence: 99%

Introduction to quantum optics

Man’ko¹

1996

AIP Conference Proceedings

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The theory of quantum propagator and time-dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Qfunction, and coherent state representation. Propagators and wave functions of a free particle, harmonic oscillator, and the oscillator with varying frequency are studied using time-dependent linear in position and momentum integrals of motion. Such nonclassical states of light (of quantum systems) as squeezed states, correlated states, even and odd coherent states (Schrödinger cat states) are considered. Photon distribution functions of Schrödinger cat male and female states are given, and the photon distribution function of squeezed vacuum is derived using the theory of the oscillator with varying parameters. Properties of multivariable Hermite polynomials used for the description of the multimode squeezed and correlated light and polymode Schrödinger cats are studied.

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“…It is important to study the Schrödinger uncertainty relation [54] in the framework of the new approach. Linear integrals of motion for quadratic systems [55,56] are useful to obtain the propagator of the new evolution equation for the marginal distribution [57]. The new approach can be also applied to study nonlinear coherent states [58,59,60].…”

Section: Quantum Measurements and Collapse Of Wave Functionmentioning

confidence: 99%

Conventional quantum mechanics without wave function and density matrix

Man’ko¹

1999

AIP Conference Proceedings

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The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schrödinger evolution equation and to the energy level equation written for the positive probability distribution are discussed. Instead of the transition probability amplitude (Feynman path integral) a transition probability is introduced. A new formulation of the conventional quantum mechanics (without wave function and density matrix) based on the "probability representation" of quantum states is given. An equation for the propagator in the new formulation of quantum mechanics is derived. Some paradoxes of quantum mechanics are reconsidered.

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Coherent States and Transition Probabilities in a Time-Dependent Electromagnetic Field

Cited by 202 publications

References 21 publications

Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field

Class of invariants for the two-dimensional time-dependent Landau problem and harmonic oscillator in a magnetic field

Introduction to quantum optics

Conventional quantum mechanics without wave function and density matrix

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