之前文章的延拓。

EJP-105367.pdf   

没想到这次编辑送了四个审稿人。有两个意见很长。要花大力气修改了。

Reviewer’s report.pdf

Report on EJP105-367.pdf

Dear Dr Zhang,

Re: "An exactly solvable toy model whose spectrum is topological" by Wang, XunGao; Zhang, Jiang min

Article reference: EJP-105367

We have now received the referee report(s) on your Paper, which is being considered by European Journal of Physics. I apologise for the delay in getting a decision back to you.

The referee(s) have recommended that you make substantial changes to your article. The referee report(s) can be found below and attached to this message. You can also access the reports at your Author Centre, at https://mc04.manuscriptcentral.com/ejp-eps

Please consider the referee comments and amend your article according to the recommendations. You should then send us a clean final version of your manuscript. Please also send (as separate files) point-by-point replies to the referee comments  including a list of changes you have made and an additional copy of your manuscript with the changes highlighted (for further information visit https://publishingsupport.iopscience.iop.org/questions/how-to-prepare-your-revised-article/). This will aid our referees in reviewing your revised article. Please upload the final version and electronic source files to your Author Centre by 01-Sep-2020.

If we do not receive your article by this date, it may be treated as a new submission, so please let us know if you will need more time.

Please note that if the referee(s) and Editorial Board are not satisfied with the changes to your manuscript, it may still be rejected.

Should your Paper be accepted for publication we would also like to invite you to create a video abstract to accompany your article, in order to further increase its visibility and impact.

Video abstracts are short, filmed overviews of the main outcomes of your paper and should enable you to go beyond the constraints of your written article to allow you to personally explain the importance of your work to the journal's global audience. Papers with video abstracts often receive more downloads than those papers without.

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We look forward to hearing from you soon.

Yours sincerely

Lucy Joy

On behalf of the IOP peer-review team:

Jessica Thorn - Editor 

Lucy Joy – Associate Editor 

Joanna Bewley and Cat McRoberts – Editorial Assistants

ejp@ioppublishing.org

and Ian Forbes – Publisher

IOP Publishing

Temple Circus, Temple Way, Bristol

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www.iopscience.org/ejp 

2018 Impact Factor: 0.861

REFEREE REPORT(S):

Referee: 1

COMMENTS TO THE AUTHOR(S)

The paper aims on a special toy model related to quantum physics teaching for undergraduate students level.

It highlights some original (Toeplitz matrix) features and derivations from the view point of Dirac equation /operator model, and shows a distinct analytic solution for the given toy mode problem.

 The author should think about the bigger context of such approaches, also the relationship to non-selfajoined operators, e.g http://www.mathematik.uni-muenchen.de/~cuenin/Habil_overviewonly or  in context of  Riesz transfrom and orbital angular momentum models,

Referee: 2

COMMENTS TO THE AUTHOR(S)

This paper needs previous reading of EJP 40 (2019) 035401 and probably they could have been  just one paper. They are very relevant together. Besides, some notation would be modified: \theta for Heaviside function and angular variables. Authors must add a \Delta symbol into equation 5. On the other hand, to introduce research problems as an exercise to undergraduate students have great value.

Referee: 3

COMMENTS TO THE AUTHOR(S)

See comments in separate file - 'Report on EJP105-367.pdf'

Referee: 4

COMMENTS TO THE AUTHOR(S)

The Paper falls within the scope of the EJP and the motivation and relevance of the research are quite important. The authors have presented  the exactly solvable toy model in “an attempt to regularize a previously known exactly solvable model” [Yang and Zhang, Eur. J. Phys. 40, 035401 (2019)].  The interesting feature of the  model is related to the fact that “while the Hamiltonian of the model is parameterized by some function f(x), its “spectrum depends only on the end values of the function f”. Finally, the authors state that the “model can serve as a good exercise in quantum mechanics at the undergraduate level”. 

The paper is very interesting and adds to results that are already published.  Obviously, it will be accepted by readers (undergraduate students, PhD students et al ) with a great interest.  However, there are a few points, which should be clarified to meet the possible questions of the readers (see the attached total Reviewer's report - 'Reviewer’s report.pdf')

Conclusion: The scientific and methodical merits of the paper are quite high; the paper contains useful material for audience at advanced undergraduates and above and can be recommended for publication in the EJP provided the authors have complied with the points listed in the report.