Exact Propagators for Soliton Potentials

Pupasov, Andrey

doi:10.3842/sigma.2005.020

Cited by 6 publications

(9 citation statements)

References 15 publications

(30 reference statements)

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“…In particular, explicit expressions for propagators are collected in [261], an excellent account of exactly solvable path integral problems. A recent extension of some of these results exploits methods of supersymmetric quantum mechanics [267,268,269]. Finally, one should mention representations of the retarded time-dependent Green function as expansions involving resonant states [280,287], which are summarized in Appendix E.…”

Section: Final Commentsmentioning

confidence: 99%

Quantum transients

2009

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Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions. Examples are diffraction in time, buildup processes, decay, trapping, forerunners or pulse formation, as well as other phenomena recently discovered, such as the simultaneous arrival of a wave peak at arbitrarily distant observers. The interest on these transients is nowadays enhanced by new technological possibilities to control, manipulate and measure matter waves.Comment: review article, 76 pp, 36 figures, more content, typos correcte

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Section: Final Commentsmentioning

confidence: 99%

Quantum transients

2009

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“…The −tanh(x(t)) corresponds to a potential of the form 1 − 2/cosh(x) 2 -fundamental solution not so trivial. 19 esech…”

Section: Example: Beněsmentioning

confidence: 99%

Supersymmetry and nonlinear filtering: operator perspective

Balaji

2014

SPIE Proceedings

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Supersymmetry (SUSY), or Bose-Fermi symmetry, is an attempt to provide a unified description of all of the fundamental interactions. Although originally introduced in the quantum field theory context, it was noted by Witten that the understanding of certain features of SUSY was simpler in the quantum mechanical setting. Some aspects of the vast subject of supersymmetric quantum mechanics, and the supersymmetric Fokker-Planck equation, of relavance to continuous-time nonlinear filtering theory are briefly reviewed. The applicability of certain remarkable results in supersymmetric quantum mechanics to nonlinear filtering is noted and illustrated with a few examples.

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“…Operator L maps the oscillator eigen-functions (8) to the eigen-functions of the rationally extended oscillator…”

Section: Harmonic Oscillator Hermite Polynomials and Potentials With ...mentioning

confidence: 99%

“…In the case of shape-invariant potentials, relations between propagators were studied in [6,7]. A more general approach for the calculations of propagators for potentials generated by an arbitrary chain of Darboux transformations were developed in [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%