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Europhysics Letters (EPL)

Reply to the Comment by P. Bosso and S. Das

Harshit Verma, Toshali Mitra, Bhabani Prasad Mandal

Published Jan 29, 2019• 0 citations

Abstract

Introduction.-Through this document, we wish to respond to the comments [1] made on our manuscript entitled "Schwinger's model of angular momentum with GUP".First of all, the authors have wrongly presumed that we have invalidated/questioned their results in [2].In the abstract section, they claim that their work is valid, on which, we made no claims suggesting the contrary in the paper [3].In fact we have used some of their results in our work.The only issue which we found was that the Clebsch-Gordan (CG) coefficients for the same state, obtained in their work by applying J -and J + operators were different.This is clearly unacceptable.This situation can be better described with the word "inconsistency" rather than with the word, "ambiguous".We feel that there was, in fact, no ambiguity in the mathematical calculations of CG coefficients using the operators J -and J + in their works.In our work we have removed this inconsistency.Now, we shall try to address the specific points raised by the authors.

DOI: 10.1209/0295-5075/125/10003

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Schwinger's model of angular momentum with GUP

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Comment on “Schwinger's model of angular momentum with GUP” by Verma Harshit et al .

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In this note, we show that the methodology and conclusions of "Schwinger's Model of Angular Momentum with GUP" [arxiv:1808.00766] are flawed and that the conclusions of "Generalized Uncertainty Principle and angular momentum" (P. Bosso and S. Das) [arxiv:1607.01083] remain valid.

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Introduction.-Through this document, we wish to respond to the comments [1] made on our manuscript entitled "Schwinger's model of angular momentum with GUP".First of all, the authors have wrongly presumed that we have invalidated/questioned their results in [2].In the abstract section, they claim that their work is valid, on which, we made no claims suggesting the contrary in the paper [3].In fact we have used some of their results in our work.The only issue which we found was that the Clebsch-Gordan (CG) coefficients for the same state, obtained in their work by applying J -and J + operators were different.This is clearly unacceptable.This situation can be better described with the word "inconsistency" rather than with the word, "ambiguous".We feel that there was, in fact, no ambiguity in the mathematical calculations of CG coefficients using the operators J -and J + in their works.In our work we have removed this inconsistency.Now, we shall try to address the specific points raised by the authors.

We study the generalized uncertainty principle (GUP) modified simple harmonic oscillator (SHO) in the operator formalism by considering the appropriate form of the creation and annihilation operators . The angular-momentum algebra is then constructed using Schwinger's model of angular momentum with two independent GUP modified SHOs. With the GUP modified angular-momentum algebra, we discuss coupling of angular momentum for a two-particle composite system. Further, we calculate the Clebsch-Gordan (CG) coefficients for a two-particle system explicitly. Our results show that the CG coefficients do not receive any corrections up to quadratic GUP.

The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.