Quantum scattering from a class of anisotropic potentials

Gravador, E.; Carpio-Bernido, M. Victoria; Bernido, Christopher C.

doi:10.1016/s0375-9601(99)00773-2

Cited by 5 publications

(8 citation statements)

References 9 publications

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“…One technique that is often overlooked when it comes to solving non-relativistic quantum mechanical dynamics is the Feynman path integral method, which has been widely used in high energy physics, quantum field theory, and statistical mechanics. However, it is not always a researcher's first instinct for fundamental physics problems [36][37][38][39][40][41][42][43][44]. Based on a Lagrangian approach, the formal path integral technique yields results completely equivalent to the Hamiltonian-based Schrödinger equation approach [45].…”

Section: Introductionmentioning

confidence: 99%

Recovery time of matter Airy beams using the path integral quantum trajectory model

2019

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Following their discovery in the late 1970s, optical Airy beams have found numerous applications in technologies such as microscopy and optical trapping, many of which are based on the wave packets' unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recent advancements have shown that Airy beams can also be produced using matter waves with many of the same unique characteristics of their optical counterparts. We present here a study of the recovery time of damaged matter Airy wave packets in free space and a nonlinear Kerr-type medium. We show that in free space the recovery time increases approximately linearly with mass and is independent of other kinematical parameters such as momentum, velocity, and spatial width. In the Kerr-type medium, recovery time is decreased compared to free space and does not scale linearly with mass. In order to study matter Airy beams, we introduce the Path Integral Quantum Trajectory model as a new computational tool for the study of non-relativistic, quantum mechanical wave packets and demonstrate its effectiveness in dealing with heavy particle dynamics.

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Section: Introductionmentioning

confidence: 99%

Recovery time of matter Airy beams using the path integral quantum trajectory model

2019

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“…At the end, we remark that potentials (7) and ( 8) belong to a class of superintegrable potentials [29]. The scattering problems for these potentials have been investigated by the path integral method in [30]. Those authors do not discuss the transparency phenomenon.…”

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confidence: 99%

“…Those authors do not discuss the transparency phenomenon. However, from equations ( 19) and ( 21) of [30] one may conclude that the potentials under consideration are transparent. For example, putting α = γ = 0 and β = (4n 2 − 1)/8 in (1) of [30] we come to the potential in (8).…”

mentioning

confidence: 99%

“…However, from equations ( 19) and ( 21) of [30] one may conclude that the potentials under consideration are transparent. For example, putting α = γ = 0 and β = (4n 2 − 1)/8 in (1) of [30] we come to the potential in (8). In this case the S-matrix (see equation ( 19) of [30]) is reduced to…”

mentioning

confidence: 99%

“…For example, putting α = γ = 0 and β = (4n 2 − 1)/8 in (1) of [30] we come to the potential in (8). In this case the S-matrix (see equation ( 19) of [30]) is reduced to…”

mentioning

confidence: 99%

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