Classical analog to the Airy wave packet

Matulis, A.; Acus, A.

doi:10.3952/physics.v59i3.4078

Cited by 3 publications

(4 citation statements)

References 9 publications

(11 reference statements)

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“…It is interesting to show how the very well-known Airy wave packets [4,5,[11][12][13][14][15] is obtained in our formalism. We prove below that the acceleration experienced by these wave packets is due to the Bohm potential.…”

Section: B Accelerating Airy Wave Packetsmentioning

confidence: 91%

A new approach to solving the Schrödinger equation

Hojman¹,

Asenjo²

2020

Preprint

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A new approach to find exact solutions to one-dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. The potential function defines the amplitude and the phase of any wavefunction which solves the one-dimensional Schrödinger equation. This new approach allows us to recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions that have vanishing and non-vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some unexpected and surprising quantum results which seem to (but do not) violate the correspondence principle such as accelerated Airy wavefunctions which solve the free Schrödinger equation, are due to the presence of non-vanishing Bohm potentials. New examples of this kind are found and discussed. The relation of these results to some of the unusual solutions to other wave equations is briefly discussed.

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Section: B Accelerating Airy Wave Packetsmentioning

confidence: 91%

A new approach to solving the Schrödinger equation

Hojman¹,

Asenjo²

2020

Preprint

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“…We will focus mainly on the second type of dispersion that comes from the cutoff frequency and allows us to introduce a simpler continuous version of the problem, making the transition to the limit a → 0. Thus, replacing the mass number by the coordinate x = a, and the energy of the primitive cell by the density of energy E(x) = E /a, introducing new constants ρ = /a, G = κ/a, T = ξa, c = aω 0 = / T ρ , (9) and variables…”

Section: Energy and Its Flowmentioning

confidence: 99%

“…Gous-sev's paper [8] asserts that the effect of the negative probability flow occurs not only for a free quantum particle, but also for an ensemble of free classical particles with a Gaussian distribution of positions and momenta. This is quite expectable because the particle ensemble always shows a greater variety of motion types than the movement of an individual particle [9].…”

Section: Introductionmentioning

confidence: 99%

Negative flow of energy in a mechanical wave

Matulis¹,

Acus²

2020

Lith. J. Phys.

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A classical system, which is analogous to the quantum one with a backﬂow of probability, is proposed. The system consists of a chain of masses interconnected by springs and attached by other springs to ﬁxed supports. Thanks to the last springs the cutoﬀ frequency and dispersion appears in the spectrum of waves propagating along the chain. It is shown that this dispersion contributes to the appearance of a backﬂow of energy. In the case of the interference of two waves, the magnitude of this backﬂow is an order of magnitude higher than the value of probability backﬂow in the mentioned quantum problem. The equation of Green’s function is considered and it is shown that the backﬂow of energy is also possible when the system is excited by two consecutive short pulses. This classical backﬂow phenomenon is explained by the branching of energy ﬂow to local modes that is conﬁrmed by the results for the forced damped oscillator. It is shown that even in such a simple system the backﬂow of energy takes place (both instantaneous and average).

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“…Goussev's paper [5] asserts that the effect of the negative probability flow occurs not only for a free quantum particle, but also for an ensemble of free classical particles with a Gaussian distribution of positions and momenta. This is quite expectable because the particle ensemble always shows a greater variety of motion types than the movement of an individual particle [6].…”

Section: Introductionmentioning

confidence: 99%

Negative flow of energy in a mechanical wave

Matulis,

Acus

2020

Preprint

View full text Add to dashboard Cite

A classical system, which is analogous to the quantum one with a backflow of probability, is proposed. The system consists of a chain of masses interconnected by springs, as well attached by other springs to fixed supports. Thanks to the last springs the cutoff frequency and dispersion appears in the spectrum of waves propagating along the chain. It is shown that this dispersion contributes to the appearance of a backflow of energy. In the case of the interference of the two waves, the magnitude of this backflow is an order of magnitude higher than the value of the probability backflow in the mentioned quantum problem. The equation of Green's function is considered, and it is shown that the backflow of energy is also possible when the system is excited by two consecutive short pulses. This classical backflow phenomenon is explained by the branching of energy flow to local modes, what is confirmed by the results for the forced damped oscillator. It is shown that even in such a simple system the backflow of energy takes place (both an instantaneous and on average) and the energy comes back to external force.

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Classical analog to the Airy wave packet

Cited by 3 publications

References 9 publications

A new approach to solving the Schrödinger equation

A new approach to solving the Schrödinger equation

Negative flow of energy in a mechanical wave

Negative flow of energy in a mechanical wave

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