Quantum particle displacement by a moving localized potential trap

Granot, Er'el; Marchewka, Avi

doi:10.1209/0295-5075/86/20007

Cited by 17 publications

(32 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also call Φ( r) the initial wave function at t = 0 (for the specific case studied in Ref. [1] this is the wave function of the ground state).…”

Section: Spectral Decompositionmentioning

confidence: 99%

“…where θ ≡ v/γ is the adiabatic Massey parameter [10,1]. Clearly, the probability that the particle remains in the bound state of the moving well is simply given by…”

Section: Attractive Dirac Delta Potentialmentioning

confidence: 99%

“…In a recent paper, Ref. [1], Granot and Marchewka have studied the interesting problem of determining the behavior of a quantum particle trapped in a localized potential, when the potential suddenly starts to move at constant speed at t = 0. These authors used an attractive Dirac delta potential in one dimension to model the problem, calculating exactly the probability that the particle remains confined to the moving potential or that it remains in the initial position.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum particles in a moving potential

Ahumada-Centeno¹,

Amore²,

Fernández³

et al. 2020

Phys. Scr.

View full text Add to dashboard Cite

We study the behavior of a quantum particle, trapped in localized potential, when the trapping potential starts suddenly to move with constant velocity. In one dimension we have reproduced the results obtained by Granot and Marchewka, Ref.[1], for an attractive delta function, using an approach based on a spectral decomposition, rather than on the propagator. We have also considered the cases of Pöschl-Teller and simple harmonic oscillator potentials (in one dimension) and to the hydrogen atom (in three dimensions). In this last case we have calculated explicitly the leading contribution to the ionization probability for the hydrogen atom due to a sudden movement.

show abstract

“…We also call Φ( r) the initial wave function at t = 0 (for the specific case studied in Ref. [1] this is the wave function of the ground state).…”

Section: Spectral Decompositionmentioning

confidence: 99%

“…where θ ≡ v/γ is the adiabatic Massey parameter [10,1]. Clearly, the probability that the particle remains in the bound state of the moving well is simply given by…”

Section: Attractive Dirac Delta Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum particles in a moving potential

Ahumada-Centeno¹,

Amore²,

Fernández³

et al. 2020

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The time dependence of the Dirac delta potentials could also be expressed through the motion of its support [45]. As a physical application, a moving Dirac δ potential is used to describe particle displacement using a standard tunneling microscope [46].…”

Section: Introductionmentioning

confidence: 99%

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

2020

View full text Add to dashboard Cite

We study the time-dependent Schrödinger equation with finite number of Dirac δ and δ ′ potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrödinger equation for δ ′ potential with particular forms of the strengths.

show abstract

“…[11] and [12]. These are examples of the general class of transient quantum processes, which occur in diverse physical settings and have numerous applications, as reviewed in a recent article [13].…”

Section: Introductionmentioning

confidence: 99%

Trapping of quantum particles and light beams by switchable potential wells

Sonkin

Malomed²,

Granot³

et al. 2010

Phys. Rev. A

View full text Add to dashboard Cite

We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as scanning tunneling microscopy or photo-switchable quantum dots. The same models, based on the linear Schrödinger equation with time-dependent trapping potentials, apply to the description of optical planar systems designed for the switching of trapped light beams. The analysis is carried out in the analytical form, using exact solutions of the Schrödinger equation. The first dynamical problem considered in this work is the retention of a particle released from a trap which was suddenly turned off, while another local trap was switched on at a distance-immediately or with a delay. In this case, we demonstrate that the maximum of the retention rate is achieved at a specific finite value of the strength of the new trap, and at a finite value of the temporal delay, depending on the distance between the two traps. Another problem is retrapping of the bound particle when the addition of the second trap transforms the single-well setting into a double-well potential (DWP). In that case, we find probabilities for the retrapping into the ground or first excited state of the DWP. We also analyze effects entailed by the application of a kick to a bound particle, the most interesting one being a kick-induced transition between the DWP's ground and excited states. In the latter case, the largest transition probability is achieved at a particular strength of the kick.

show abstract

Quantum particle displacement by a moving localized potential trap

Cited by 17 publications

References 16 publications

Quantum particles in a moving potential

Quantum particles in a moving potential

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

Trapping of quantum particles and light beams by switchable potential wells

Contact Info

Product

Resources

About