The quantum square well with moving boundaries: A numerical analysis

Fojón, O A; Gadella, M.; Lara, Luis

doi:10.1016/j.camwa.2009.09.011

Cited by 22 publications

(49 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…

In this comment we show that the approach presented by Fojón et al [1] is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which the authors criticize, proves to be considerably better.

…”

mentioning

confidence: 52%

Comment to: "The quantum square well with moving boundaries: a numerical analysis"

Ahumada-Centeno,

Amore,

Fernandez

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…

…”

mentioning

confidence: 52%

Comment to: "The quantum square well with moving boundaries: a numerical analysis"

Ahumada-Centeno,

Amore,

Fernandez

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…They form a complete orthogonal set at any fixed time and the expectation value of the energy E φn (t) = 0 φ * n (−∂ 2 x φ n )dx = (nπ/ ) 2 . System (16) and its solutions (17) were also discussed in [17][18][19][20]. In Fig.…”

Section: Infinite Square-well Potential With a Moving Barriermentioning

confidence: 99%

Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier

Contreras-Astorga

Hussin

2019

Integrability, Supersymmetry and Coherent States

View full text Add to dashboard Cite

Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional particle in a box. With a point transformation, an infinite square-well potential with a moving barrier is generated. Using time dependent supersymmetry, the latter leads to a trigonometric Pöschl-Teller potential with a moving barrier. Finally, a confluent time dependent supersymmetry transformation is implemented to generate new infinite potential wells, all of them with a moving barrier. For all systems, solutions of the corresponding time dependent Schrödinger equation fulfilling boundary conditions are presented in a closed form.

show abstract

“…A recent numerical study of a particle in a box with different laws for the movement of the wall show that physical quantities like probability density and expectation value of position or mean value of the energy have a smooth behavior for small speed of the moving wall. In contrast, if this speed becomes large, many irregularities appears as sharp bumps on the probability distribution or a chaotic shape on the averaged values of position and energy [9].…”

Section: Introductionmentioning

confidence: 96%

Quantum effective force in an expanding infinite square-well potential and Bohmian perspective

Mousavi¹

2012

Phys. Scr.

View full text Add to dashboard Cite

The Schrödinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though the particle is nowhere near the walls, it will be affected. It is shown that this force apart from a minus sign is equal to the expectation value of the gradient of the quantum potential for vanishing at the walls boundary condition. Variation of this force with time is studied. A selection of Bohmian trajectories of the confined particle is also computed.

show abstract

The quantum square well with moving boundaries: A numerical analysis

Cited by 22 publications

References 15 publications

Comment to: "The quantum square well with moving boundaries: a numerical analysis"

Comment to: "The quantum square well with moving boundaries: a numerical analysis"

Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier

Quantum effective force in an expanding infinite square-well potential and Bohmian perspective

Contact Info

Product

Resources

About