SUSUSY quantum mechanics

CINVESTAV); David J. Fernandez C. (Physics Department

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SUSUSY quantum mechanics

David J. Fernandez C. (Physics Department, CINVESTAV)

Quantum Physics · Submitted 14 Sep 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials as a particular case.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,155 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.42 · compares with prior results 0.83 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials as a particular case.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators".	background 1.00	0.05	0.03	asserted 0.99
s1	In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order.	background 1.00	0.09	0.04	asserted 1.00
s2	In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators.	contribution 0.76	0.87	0.38	asserted 0.94
s3	The links between this method and SUSY are analysed.	contribution 0.95	0.81	0.06	asserted 0.81
s4	As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials as a particular case.	result 0.92	0.91	0.32	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 1.00.

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sources read

arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials as a particular case.

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8 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 8 sentences without a confident label

Cites it as background 2 papers

A higher order generalization of the Darboux transformations, known as the Darboux-Crum transformations [ref] , gives rise to a higher derivative generalization of supersymmetric quantum mechanics [ref] , characterized by nonlinear superalgebraic relations [ref] .

Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry · Introduction · 0.87
A supersymmetric quantum mechanical system is characterized by supercharges which can be differential operators of the first [ref] or higher [ref] order.

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis · Introduction · 1.00

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