Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

P. Roy; T.K. Jana

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Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

T.K. Jana, P. Roy

Quantum Physics · Submitted 12 Aug 2009

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

The authors' main claim The spectrum in both the cases are found to be real.

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The compiled record

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.06 · 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.

We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $\eta$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.

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	We study non-Hermitian quantum mechanics in the presence of a minimal length.	contribution 0.86	0.89	0.05	asserted 0.79
s1	In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty.	contribution 0.91	0.95	0.16	asserted 1.00
s2	The spectrum in both the cases are found to be real.	result 1.00	0.94	0.42	asserted 1.00
s3	It is also shown that the models are $\eta$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.	result 0.85	0.94	0.24	asserted 1.00

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

What was examined, and what was not

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arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
relations to other papers

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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

We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $\eta$ pseudo-Hermitian and the metric operator is found explicitly in both the cases.

Human review

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How the literature uses it

4 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

We demonstrate that the recent paper by Jana and Roy entitled ''Non-Hermitian quantum mechanics with minimal length uncertainty'' [SIGMA 5 (2009), 083, 7 pages, arXiv:0908.1755] contains various misconceptions.

Comment on "Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty" · 0.93

Papers citing it · 5 sentences without a confident label

Compares with it 1 paper

In a certain limit, as specified in [ref] , $X$ and $P$ allow for a well-known representation of the form $X=(1+τp_0^2)x_0$ and$P=p_0$, which in momentum space, i.e. $x_0=iħ∂_p_0$, corresponds to the one used by Jana and Roy [ref] , up to an irrelevant additional term $iħγ̃P$.

Comment on "Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty" · Introduction · 0.92

Cites it as background 2 papers

This pure GUP effect has been treated in the framework of the perturbation expansion using the naive coordinate representation and discussed in detail for various quantum systems (see Refs. [ref] without the quest of completeness), among others for the particle in a box [ref] .

Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics · Introduction · 0.94
This direct GUP effect has been treated in the framework of the perturbation expansion using the coordinate representation and discussed in detail for various quantum systems (see Refs. [ref] without the quest of completeness), among others for the particle in a box [ref] .

Particle in a cavity in one-dimensional bandlimited quantum mechanics · Introduction · 0.90

What it cites · 21 sentences without a confident label

Cites as background 6 papers

We recall that a Hamiltonian $H$ is called $η$ pseudo-Hermitian if it satisfies the condition [ref] [equation] where $η$ is a Hermitian operator.

Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian · $η$ pseudo-Hermiticity · 0.96
On the other hand, since the work of Bender et al. [ref] non-Hermitian quantum systems have been studied extensively over the past few years[See <http://gemma.ujf.cas.cz/ znojil/conf/>.].

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry · Introduction · 0.97
In recent years there have been growing interest on quantum systems with a minimal length [ref] .

Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry · Introduction · 1.00

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