Scattering states of the Sech-squared potential

Tong, B. Y.

doi:10.1016/s0038-1098(97)10009-6

Cited by 29 publications

(14 citation statements)

References 8 publications

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“…The Pöschl-Teller (PT) potential has been studied since the early days of quantum mechanics (see, e.g., [61]); it has been applied in the context of semiconductor quantum wells [62][63][64], and it can be used to model nonlinear optical properties [65,66].…”

Section: Pöschl-teller Potentialmentioning

confidence: 99%

Nonlinearity as a resource for nonclassicality in anharmonic systems

et al. 2016

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Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing -which is not captured by the negativity of the Wigner function -we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators. II. NONCLASSICALITY OF A STATE AND NONLINEARITY OF A POTENTIALA. Nonclassicality of a Single-mode Bosonic StateWe consider a bosonic system with a single degree of freedom, such as a one-dimensional oscillator or a single-mode of

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Section: Pöschl-teller Potentialmentioning

confidence: 99%

Nonlinearity as a resource for nonclassicality in anharmonic systems

et al. 2016

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“…Let us consider two comparison potentials: the cut-off Coulomb potential V a [21,22], which has a known analytical solution [14], and the sech-squared potential V b [23][24][25][26] …”

Section: An Examplementioning

confidence: 99%

Sharp comparison theorems for the Klein–Gordon equation in d dimensions

Hall

Zorin

2016

Int. J. Mod. Phys. E

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We establish sharp (or 'refined') comparison theorems for the Klein-Gordon equation. We show that the condition Va ≤ V b , which leads to Ea ≤ E b , can be replaced by the weaker assumption Ua ≤ U b which still implies the spectral ordering Ea ≤ E b . In the simplest case, for d = 1,Vi(t)dt, i = a or b, and for d > 1, Ui(r) = r 0 Vi(t)t d−1 dt, i = a or b. We also consider sharp comparison theorems in the presence of a scalar potential S (a 'variable mass') in addition to the vector term V (the time component of a 4-vector). The theorems are illustrated by a variety of explicit detailed examples.

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“…) dx dp; (15) when the two interference patterns are displaced by a tile, one has a destructive interference effect, the above integration tends to zero and the two states become quasiorthogonal. Thus, the size of sub-Planck structures sets a sensitivity limit on probing small potential modifications.…”

Section: Sensitivity Of Sub-planck Scale Structuresmentioning

confidence: 99%

Sub-Planck-scale structures in the Pöschl-Teller potential and their sensitivity to perturbations

et al. 2009

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We find the existence of sub-Planck scale structures in the Pöschl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner distribution of the state evolved from an initial coherent state up to various fractional revival times. We also investigate the sensitivity to perturbations of the Pöschl-Teller potential and we verify that, similar to the harmonic oscillator, the presence of sub-Planck structure in phase space is responsible for a high sensitivity to phase-space displacements.

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Scattering states of the Sech-squared potential

Cited by 29 publications

References 8 publications

Nonlinearity as a resource for nonclassicality in anharmonic systems

Nonlinearity as a resource for nonclassicality in anharmonic systems

Sharp comparison theorems for the Klein–Gordon equation in d dimensions

Sub-Planck-scale structures in the Pöschl-Teller potential and their sensitivity to perturbations

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