Klein-Gordon particle in a one-dimensional box with a moving wall

Hamidi, Omid; Dehghan, Hossein

doi:10.1016/s0034-4877(14)60029-x

Cited by 4 publications

(8 citation statements)

References 9 publications

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“…The disappearance of Klein tunneling in the infinite well limit should also be of interest to recent works that have studied the Klein-Gordon equation in a box with moving walls [14][15][16] (the special boundary conditions chosen in these works were indeed not justified).…”

Section: Discussionmentioning

confidence: 99%

Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox

Alkhateeb,

Matzkin

2021

Preprint

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The "particle in a box" problem is investigated for a relativistic particle obeying the Klein-Gordon equation. To find the bound states, the standard methods known from elementary non-relativistic quantum mechanics can only be employed for "shallow" wells. For deeper wells, when the confining potentials become supercritical, we show that a method based on a scattering expansion accounts for Klein tunneling (undamped propagation outside the well) and the Klein paradox (charge density increase inside the well). We will see that in the infinite well limit, the wavefunction outside the well vanishes and Klein tunneling is suppressed: quantization is thus recovered, similarly to the non-relativistic particle in a box. In addition, we show how wavepackets can be constructed semianalytically from the scattering expansion, accounting for the dynamics of Klein tunneling in a physically intuitive way.

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Section: Discussionmentioning

confidence: 99%

Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox

Alkhateeb,

Matzkin

2021

Preprint

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“…Therefore this amounts to what is called the ultra non-relativistic limit and the above solution represent a negative energy solutions for which E ≈ −mc 2 . Note that it is best to use the functions J iν (z) sin(φ n ) and J −iν (z) sin(φ n ), also the basis used in [15], as they form the right basis for the emergence of non-relativistic solutions.…”

Section: Discussionmentioning

confidence: 99%

“…The analytical solutions of this problem (a KG particle in an infinite square-well potential with a linearly expanding wall) were obtained by Koehn (see eq. 11 in [13]); other authors proposed a generalization shortly after [14], and gave an alternative method in [15]. These solutions can be written as linear superpositions of with n = 1, 2, 3, .…”

Section: Kg Equation With a Moving Boundarymentioning

confidence: 99%

“…The goal of the present article is precisely to answer this question by investigating the same system in a relativistic setting based on the Klein-Gordon (KG) equation. We will rely on the solutions of the KG equation for a particle inside a uniformly expanding cavity that were recently obtained [13][14][15]. As is well-known, the KG equation is not free of interpretation problems, but we will consider a regime in which these problems do not appear.…”

Section: Introductionmentioning

confidence: 99%

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Non-locality and time-dependent boundary conditions: a Klein-Gordon perspective

Colin,

Matzkin

2020

Preprint

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The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the relativistic wavefunction. We show that this expansion induces a non-local effect on the current density throughout the cavity. Our results indicate that a relativistic treatment still contains apparently spurious effects traditionally associated with the unbounded velocities inherent to non-relativistic solutions obtained from the Schrödinger equation. Possible reasons for this behaviour are discussed.

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“…The goal of the present article is precisely to answer this question by investigating the same system in a relativistic setting based on the Klein-Gordon (KG) equation. We will rely on the solutions of the KG equation for a particle inside a uniformly expanding cavity that were recently obtained [13][14][15]. Note that several properties of singleparticle relativistic wave equations have been investigated recently [16][17][18][19].…”

mentioning

confidence: 99%

Non-locality and time-dependent boundary conditions: A Klein-Gordon perspective

Colin¹,

Matzkin²

2020

EPL

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The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single-particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the relativistic wave function. We show that this expansion induces a non-local effect on the current density throughout the cavity. Our results indicate that a relativistic treatment still contains apparently spurious effects traditionally associated with the unbounded velocities inherent in non-relativistic solutions obtained from the Schrödinger equation. Possible reasons for this behaviour are discussed.

show abstract

Klein-Gordon particle in a one-dimensional box with a moving wall

Cited by 4 publications

References 9 publications

Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox

Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox

Non-locality and time-dependent boundary conditions: a Klein-Gordon perspective

Non-locality and time-dependent boundary conditions: A Klein-Gordon perspective

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