Analytic Results for Gaussian Wave Packets in Four Model Systems: I. Visualization of the Kinetic Energy

Robinett, R. W.; Bassett, Lee C.

doi:10.1007/s10702-004-1117-9

Cited by 16 publications

(24 citation statements)

References 34 publications

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“…2 (obtained without taking into acount f (x 0 , p 0 , t)). In fact, having μ = 0 corresponds to take θ = 0 in (27) and (29); consequently, we obtain the solution (13), since lim The most interesting situation, however, is to allow μ = 0 in order to have an idea of the effect of back reaction on ρ xx . Figure 5 shows what happens for μ varying from 0 to 100.…”

Section: Back Reaction Between a Black Hole And Hawking Radiationmentioning

confidence: 99%

Indefinite oscillators and black-hole evaporation

2009

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We discuss the dynamics of two harmonic oscillators of which one has a negative kinetic term. This model mimics the Hamiltonian in quantum geometrodynamics, which possesses an indefinite kinetic term. We solve for the time evolution in both the uncoupled and coupled case. We use this setting as a toy model for studying some possible aspects of the final stage of black-hole evaporation. We assume that one oscillator mimics the black hole, while the other mimics Hawking radiation. In the uncoupled case, the negative term leads to a squeezing of the quantum state, while in the coupled case, which includes back reaction, we get a strong entangled state between the mimicked black hole and the radiation. We discuss the meaning of this state. We end by analyzing the limits of this model and its relation to more fundamental approaches. * kiefer@thp.uni-koeln.de † jmarto@ubi.pt ‡ pmoniz@ubi.pt § URL: http://www.dfis.ubi.pt/∼pmoniz ¶ Also at CENTRA, IST, Rua Rovisco Pais, 1049 Lisboa Codex, Portugal.

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Section: Back Reaction Between a Black Hole And Hawking Radiationmentioning

confidence: 99%

Indefinite oscillators and black-hole evaporation

2009

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“…[11] and [12]. This observation can also be described quantitatively by examining the distribution of kinetic energy of such a free-particle Gaussian wave packet [15]. In this approach, the standard expression for the kinetic energy is rewritten using integration-by-parts in the form…”

Section: Standard Minimum-uncertainty Gaussian Wave Packetsmentioning

confidence: 99%

Simple Examples of Position-Momentum Correlated Gaussian Free-Particle Wave Packets in One Dimension With the General Form of the Time-Dependent Spread in Position

2005

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We provide simple examples of closed-form Gaussian wave packet solutions of the free-particle Schrödinger equation in one dimension which exhibit the most general form of the time-dependent spread in position, namely (Δxtion on the position-momentum correlation structure of the initial wave packet. We exhibit straightforward examples corresponding to squeezed states, as well as quasi-classical cases, for which A < 0 so that the position spread can (at least initially) decrease in time because of such correlations. We discuss how the initial correlations in 0894-9875/05/1000-0455/0 455 these examples can be dynamically generated (at least conceptually) in various bound state systems. Finally, we focus on providing different ways of visualizing the x − p correlations present in these cases, including the time-dependent distribution of kinetic energy and the use of the Wigner quasi-probability distribution. We discuss similar results, both for the time-dependent Δx t and special correlated solutions, for the case of a particle subject to a uniform force.

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“…The most general free-particle, momentum-space and position-space Gaussian wave packets, with arbitrary initial values of x 0 = x 0 and p 0 = p 0 , can be written [30] in the form…”

Section: Free-particle Gaussian Wave Packetsmentioning

confidence: 99%

“…Using the propagator techniques outlined in [30], and the initial position-space wave function ψ(x, 0) = 1…”

Section: Simple Harmonic Oscillator Wave Packetsmentioning

confidence: 99%

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Analytic Results for Gaussian Wave Packets in Four Model Systems: II. Autocorrelation Functions

Robinett

Bassett

2004

Found Phys Lett

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The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, ψ(x, t), with its initial value, ψ(x, 0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrödinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called 'inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.

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Analytic Results for Gaussian Wave Packets in Four Model Systems: I. Visualization of the Kinetic Energy

Cited by 16 publications

References 34 publications

Indefinite oscillators and black-hole evaporation

Indefinite oscillators and black-hole evaporation

Simple Examples of Position-Momentum Correlated Gaussian Free-Particle Wave Packets in One Dimension With the General Form of the Time-Dependent Spread in Position

Analytic Results for Gaussian Wave Packets in Four Model Systems: II. Autocorrelation Functions

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