Comment on: “Ground state energies from converging and diverging power series expansions”, Ann. Phys. 373 (2016) 456-469

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• 作者：Paolo Amore^a ; ^{paolo.amore@gmail.com} ; Francisco M. Ferná ; ndez^b ; ^{fernande@quimica.unlp.edu.ar}
• 关键词：Finite attractive well ; Perturbation expansion ; Asymptotic expansion ; Periodic boundary conditions ; Square potential ; Dirac delta potential
• 刊名：Annals of Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：376
• 期：Complete
• 页码：499-504
• 全文大小：361 K
• 卷排序：376

文摘

We compare two alternative expansions for finite attractive wells. One of them is known from long ago and is given in terms of powers of the strength parameter. The other one is based on the solution of the equations of the Rayleigh–Schrödinger perturbation theory in a basis set of functions of period LL. The analysis of exactly solvable models shows that although the exact solution of the problem with periodic boundary conditions yields the correct result when L→∞L→∞ the coefficients of the series for this same problem blow up and fail to produce the correct asymptotic expansion.