正面教材分享 http://blog.sciencenet.cn/u/wdlang 70%的以色列人是无神论者,不过他们都相信上帝给了他们那块土地。这个世界经不起思考

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EJP审稿意见

已有 2728 次阅读 2020-11-1 10:48 |个人分类:审稿与投稿|系统分类:科研笔记

之前的严格可解的玩具模型的文章被EJP接收。之前有四个审稿人,这次只送给了后面两个。其中一个审稿人其实还是不太满意,不过他也妥协了。

exact_class3.pdf

虽然是个玩具模型,但是处理起来我们还是遇到了一些意外的情况。

通常量子力学教材里都会处理一维薛定谔方程中的dirac delta势。结论是大家都熟悉的,波函数连续但导数不连续。但是如果是dirac方程里的dirac delta势呢?这时候波函数本身就不连续了。有两种比较自然的想法,会得到两种不同的结果。具体见之前的博文 让人困惑的狄拉克delta函数

在现有的处理dirac方程的文章里,这两种做法都存在,大家是有争议的。

比如大家可以看看这个文章如何批评前人的做法(page 2268)

https://journals.aps.org/prc/pdf/10.1103/PhysRevC.35.2262  

在我们看来,这两个做法都合理也都不合理,真正合理的做法应该是考虑算子的self-adjoint extension。在这种观点下,两种办法不过对应于无穷种选择中比较任意的两个。

用这种观点再回头看薛定谔方程下dirac delta势的处理,就会发现,其实通常的做法也不过是在无穷种边界条件中选了一个特别的。

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REFEREE REPORT(S):

Referee: 4

COMMENTS TO THE AUTHOR(S)

The authors have accurately complied with all points listed in Referee report and improved the manuscript. Thanks to the authors for all revisions. The scientific merits of the paper are very  high. The paper should be recommended for publication in the EJP.

The issue of study of exactly solvable toy models in quantum mechanics  has nowadays attracted very considerable attention. The paper by Wang X G and Zhang J M  is the serious, highly professional attempt to develop such a model. 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.  Obviously, the paper  will be accepted by readers (undergraduate students, PhD students et al ) with a great interest.  


Referee: 3

COMMENTS TO THE AUTHOR(S)

The authors have made a serious effort to improve the readability of the paper. I believe it is still going to be a hard read for a large cross-section of EJP readers but those who will read it will learn. You may want to fix the typo in "Fourier Transform" in the second line from the top on page 4



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