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之前投到欧洲物理杂志EJP，介绍一个严格可解的玩具模型的文章收到第一轮审稿意见，两个都比较正面。

奇怪了，EJP对我一直都很友好，但AJP就不友好。之前两个投到AJP被拒的都在EJP顺利发表，而这次这个投到AJP后编辑压根没有任何反应，连个收到稿件的确认信都没有!

修改后的文章在此：

Dear Dr Zhang,

Re: "An exactly solvable toy model" by Yang, K.L; Zhang, Jiang min

Article reference: EJP-10421

We have now received the referee report(s) on your Paper, which is being considered by European Journal of Physics.

The referee(s) have recommended that you make some amendments to your article. The referee report(s) can be found below and/or 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 and either a list of changes you have made or an additional copy of your manuscript with the changes highlighted. This will aid our referees in reviewing your revised article. Please upload the final version and electronic source files to your Author Centre by 30-Jan-2019.

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.

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Stephanie White

On behalf of the IOP peer-review team:

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ejp@iop.org

and Iain Trotter – Publisher

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2017 Impact Factor: 0.642

REFEREE REPORT(S):

Referee: 1

COMMENTS TO THE AUTHOR(S)

Additional Comments (EJP-104214)

Authors: Yang K L and Zhang J M

Title: An exactly solvable toy model

The Paper falls within the scope of the EJP and the motivation and relevance of the research are quite important. The authors have analytically determined “the eigenstates and eigenenergies of a toy model, which arose in idealizing a realistic model in previous publications (Refs [1]-[3]: Zhang and Yang, EPL 114 (2016) 60001; EPL, 116 (2016) 10008; Zhang and Liu Phys. Rev. B 97 (2018) 075151 etc). The dynamic of the model is studied too, namely, the authors studied the dynamics within model considered and revisited the quench problem of Refs. [1, 2, 3]. Finally, the authors state that the “model can serve as a good exercise in quantum mechanics at the undergraduate level”.

The paper is quite interesting and adds to results that are already published. Obviously, it will be accepted by readers with an interest.

However, there are a few minor points, which should be clarified in order to meet the possible questions of the readers:

i) Obviously, It would be desirable to slightly expand the introduction of the article. It is appropriate to recall the active development of such a trend of modern computer quantum mechanics as the control of the positions of the energy levels of bound (quasi-bound) states during the transformation of potentials while maintaining the properties of symmetry. The known advances in areas such as the development of information technology, as well as micro and nanotechnology, allow to create low-dimensional structures with a predictable and controlled spectrum of charge carriers [1-6]. This progress makes perspective and relevant studies of 1-D, 2-D, 3-D dynamic quantum wells, quantum dots and lattices with localization properties. In addition, this clarifies the authors' motivation in choosing the formulation of the problem considered.

ii) The article is written extremely concisely and will be in the present form quite understandable to readers. However it is obvious that at least a brief introduction to modern exactly solvable (stationary and nonstationary) quantum-mechanical models would be very appropriate. It would be quite appropriate to remind at least briefly of widely known precisely solvable analytically (most important numerically) stationary and nonstationary problems (such as a hydrogen atom and a quantum oscillator, problems for a quantum oscillator under the action of a periodic external force, motion of a particle with spin in a uniform periodic magnetic field, and many others) [1-17].It is well known that the exact models have not only independent value, but also serve as a means of an approximate solution of inverse problems in cases when the kernels of integral equations are not degenerate. Approximation of the scattering function by fractional rational expressions corresponds to approximations of an arbitrary potential by Bargmann ones. In this case, the solutions of the inverse problem are regularized, due to the narrowing to a subset of potentials, depending on a finite number of parameters.

iii) All calculations are made by the authors quite correctly, and do not cause any serious remarks. There are only separate editorial corrections, for example: i) the authors should clearly indicate the system of physical units in which the formulas are written out; ii) Please, check that all symbols in formulas are defined; iii) It would be interesting for readers to specify possible physical applications (classical analogs) of the model.

iv) It would be appropriate to add additional important and useful (for readers) literature sources into the References List (alternative presentation of topics studied in comparison with available references) such as:

1. Ashcroft N W and Mermin N D 1976 Solid State Physics (Harcourt, New York).

2. Perelomov A M 1986 Generalized Coherent States and Their Applications (Springer, Berlin).

3. Tannor D J 2006 Introduction to Quantum Mechanics: A Time-Dependent Perspective (Univ.Science Books)

4. Akulin V M 2006 Coherent Dynamics of Complex Quantum Systems (Springer-Verlag, Berlin)

5. Glushkov A V 2008 Relativistic quantum theory. Quantum mechanics of atomic systems (Odessa: Astroprint)

6. Zakhariev B N and Suzko A A 1990 Direct and Inverse Problems: Potentials in Quantum Scattering (Springer-Verlag, Berlin)

7. Glushkov A V and Ivanov L N 1993 DC strong-field Stark effect: consistent quantum-mechanical approach J. Phys. B: At. Mol. Opt. Phys. 26 L379-386

8. Weber T A and Pursey D L 1995 Extended Gel’fand-Levitan method leading to exactly solvable Schrödinger equations with generalized Bargmann potentials Phys. Rev. A 52 3923

9. Moiseyev N 1998 Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling Phys. Rep. 302 211-293

10. Hartmann T, Keck F, Korsch H J and Mossmann S 2004 Dynamics of Bloch oscillations. New J. Phys. 6 2

11. Breid B M, , Witthaut D and H J Korsch H J Manipulation of matter waves using Bloch and Bloch–Zener oscillations2007 New J. Phys. 9 62

12. Glushkov A V, Khetselius O Yu and Malinovskaya S V 2008 Spectroscopy of cooperative laser–electron nuclear effects in multiatomic molecules. Molec. Phys. 106 1257-1260.

13. Glushkov A V, Malinovskaya S V, Khetselius O Yu, Loboda A V, Sulharev D, Lovett L 2009 Green's function method in quantum chemistry: New numerical algorithm for the Dirac equation with complex energy and Fermi‐model nuclear potential Int. J. Quant. Chem. 109 1717-1727

14. Khetselius O 2012 Spectroscopy of cooperative electron-gamma-nuclear processes in heavy atoms: NEET effect J. Phys.: Conf. Ser. 397 012012

15. Longhi S 2014 Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping EPL 106 34001

16. Chesnokov I Y and Kolovsky A R 2014 Landau-Stark states in finite lattices and edge-induced Bloch oscillations EPL 106 50001

17.Neufeld O, Sharabi Y, Ben-Asher A, Moiseyev N Calculating bound states resonances and scattering amplitudes for arbitrary 1D potentials with piecewise parabolas 2018 J. Phys. A: Math. Theor. 51 475301

v) In conclusion, perhaps the authors should slightly clarify the title of the article, for example, "On one exactly solvable toy quantum model and the quench dynamics of a Bloch state" (of course, at the discretion of the authors)!

Thanks in advance to the authors for all revisions.

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 minor points listed in the report.

Referee: 2

This paper is a beautiful short exercise in mathematical physics appropriate for advanced

undergraduates and graduate students. I recommend publication without reservations and give

a few suggestions to make the contribution even more appealing to a wider audience:

1. Although as an exercise in formal quantum theory the paper stands on its own, I believe that the

readers would be better served if the authors situated the exercise in a larger context. The

abstract does not even tell us what area of physics this toy model applies to, but only refers to

three previous publications. From one of the Journals (PRB) in which these are published one

can assume that this concerns condensed matter (CM) physics, but it would be nice to hear the

authors say so with a few more details on where this result makes a difference. A few words in

the abstract and introduction might suffice.

2. Presumably the authors are well versed in their area and could share some useful insights with

their readers. Are there many such toy models with similar solutions and if so are they limited to

CM physics? Can this particular solution method be generalized to a technique? Are there

references where one can learn these kind of skills or does one have to just admire the authors

for knowing exactly how to proceed at every step in this particular case? Presumably some

searching was involved before the solution as presented was found. Can the authors help the

readers become fluent in this field? That would definitely help justify publication in an

educational journal like EJP. Some of the answers to my questions could be added in a final

discussion section.

3. Please reassure the reader that the results obtained in Section 4 are identical (or at least

compatible with) those from refs [1‐3]. Is there anything to be learned from the fact that the

same results can be obtained through two such different methods? Which is easier? Which is

more powerful? Which gives more insight into the model?

4. Please clarify that: (a) In the infinitely many levels above Eq. (1) is n integer? (b) In Eq. (2) is g

real? (c) In Eq. (12) differentiation is w.r.t. x?

修改后审稿人意见如下，文章被接收

Referee: 2

COMMENTS TO THE AUTHOR(S)

Thanks for the changes. The paper is even more useful now.

Referee: 1

COMMENTS TO THE AUTHOR(S)

The authors have adequately taken into account all the points made in the previous report.Thanks to the authors for all revisions. The paper by Zhang, Jiang min and

Yang, K.L. should be accepted and recommended for publication in the EJP.

EJP在文章被接收后，立马就将之上线了：

http://iopscience.iop.org/article/10.1088/1361-6404/ab0389

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