Analytical solution for 3D stationary Schrödinger equation: implementation of Huygens’ principle for matter waves

Eleuch, Hichem; Rostovtsev, Yuri V.

doi:10.1080/09500340.2010.514069

Cited by 14 publications

(8 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We see that the approximate analytical solution matches well with the numerics under the parameters considered here. Extension of this methodology to Schrodinger equation [49,50] and position dependent mass Schrodinger(PDMSE) equation can be found in [51,52].…”

Section: Appendix A: Analytical Solution For Three-level Atommentioning

confidence: 99%

Ultra-short strong excitation of two-level systems

Jha

Eleuch

Grazioso

2014

Optics Communications

Self Cite

View full text Add to dashboard Cite

We present a model describing the use of ultra-short strong pulses to control the population of the excited level of a two-level quantum system. In particular, we study an off-resonance excitation with a few cycles pulse which presents a smooth phase jump i.e. a change of the pulse's phase which is not step-like, but happens over a finite time interval. A numerical solution is given for the time-dependent probability amplitude of the excited level. The control of the excited level's population is obtained acting on the shape of the phase transient, and other parameters of the excitation pulse.Comment: 6 pages, 5 figures this version is a rewriting of the previous one, with several change

show abstract

Section: Appendix A: Analytical Solution For Three-level Atommentioning

confidence: 99%

Ultra-short strong excitation of two-level systems

Jha

Eleuch

Grazioso

2014

Optics Communications

Self Cite

View full text Add to dashboard Cite

show abstract

“…The integration constants were omitted in refs. [1,4] and the solution (7) with C 2 = 0 was suggested to be applied to the case of a step potential. However, the integral in (7) contributes to f (x) an unphysical term −p exp[−2ik(x − x 0 )] in any p ′ = 0 region.…”

mentioning

confidence: 99%

“…Eqs. ( 16) of a follow up [4] of two of the authors suggest that a counter-propagating reflected plane wave was disregarded on both sides of the step.…”

mentioning

confidence: 99%

Comment on "New analytic solution of Schrödinger's equation"

Moroz

2015

Preprint

View full text Add to dashboard Cite

“…Several techniques were developed to obtain exact or approximate analytical solutions for the stationary Schrödinger equation with variable potential [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] or PDEM Schrödinger equation. [42][43][44] We can cite the point-canonical transformation, 24,25,45,46 Nikiforov-Uvarov (NU) method [45][46][47][48][49] Green's function, 50 the Heun equation, 51 the potential algebra 52 and the supersymmetric approach 53,54 as analytical methods to generate solutions for the PDEM Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%