Supersymmetry Transformations for Delta Potentials

C., David J. Fernández; Gadella, M.; Nieto, L. M.

doi:10.3842/sigma.2011.029

Cited by 5 publications

(10 citation statements)

References 68 publications

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“…These expressions generalize similar ones published in citation [14] of our Reference [15]. We see that the eigenvector depends on all the parameters (m 0 , m 1 , m 2 , m 3 , ψ).…”

Section: Self-adjoint Extensions: Determination Of Their Eigenvaluessupporting

confidence: 84%

“…Compare to Equation (68) in citation [14] of our Reference [15]. Taking into account the values of (A, B) given in ( 14) and ( 15) and also the fact that det(N (s)) = 0, the second equation of ( 18) implies that either m 3 = 0 or…”

Section: Self-adjoint Extensions: Determination Of Their Eigenvaluesmentioning

confidence: 97%

“…In particular, the construction of supersymmetric (SUSY) partners of given potentials allow for an analysis of one dimensional Hamiltonians that often keep similarities with the original ones. Many studies have been done in this field and a brief account of references [1][2][3][4][5][6][7][8][9][10][11][12][13][14] only covers a small part of all previous work.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

et al. 2021

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We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d2/dx2 on L2[−a,a], a>0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the ℓ-th order partner differs in one energy level from both the (ℓ−1)-th and the (ℓ+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of −d2/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its ℓ-th supersymmetric partners of each extension.

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“…These expressions generalize similar ones published in citation [14] of our Reference [15]. We see that the eigenvector depends on all the parameters (m 0 , m 1 , m 2 , m 3 , ψ).…”

Section: Self-adjoint Extensions: Determination Of Their Eigenvaluessupporting

confidence: 84%

Section: Self-adjoint Extensions: Determination Of Their Eigenvaluesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

et al. 2021

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“…The possibility of driving the quantum states by δ(t)-pulses of the external fields was considered by Lamb Jr. [33]. An extremely simple class of exact though formal solutions of (1) in L 2 (R) was obtained in [14,34,35,36,37] …”

Section: The Evolution Controlled By Sharp Pulsesmentioning

confidence: 99%

Quantum operations: technical or fundamental challenge?

Mielnik¹

2013

J. Phys. A: Math. Theor.

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A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as 'operation factories' transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, and some others, to verify the existence of fundamental precision limits of the position measurements or the reality of 'non-commutative geometries'.

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“…The analysis of resonances [3,4,5,6,7,8] is transparent for rectangular potentials in either, the presence of a background interaction [9,10], or in free space [11,12,13,14,15,16,17]. Simple models of point-like [18,19], as well as regularized singular interactions [20], can be obtained as limit cases of rectangular potentials [21,17,22]. The one-dimensional models are also useful in the study of supersymmetric quantum mechanics [23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time

Fernández‐García

Rosas-Ortiz

2011

SIGMA

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Abstract. We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases in which the impinging particle is 'captured' by the semi-harmonic rectangular potentials. The 'time of capture' is connected with the dwell time of the scattered wave. Using the particle absorption method, it is shown that the dwell time τ a D coincides with the phase time τ W of Eisenbud and Wigner, calculated as the energy derivative of the reflected wave phase shift. Analytical expressions are derived for the phase time τ W of the semi-harmonic delta well and barrier potentials.

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Supersymmetry Transformations for Delta Potentials

Cited by 5 publications

References 68 publications

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian

Quantum operations: technical or fundamental challenge?

Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time

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