A linear variational exercise with a simple non-orthogonal basis for the particle-in-the-box problem

The particle-in-the-box, with or without an additional potential, is proposed as an excellent laboratory to teach and explore the details of the linear variational method using a non-orthogonal basis. The xn(a - x)n and xn(a/2 - x)(a - x)n polynomials are shown to form a complete basis for the even...

Full description

Saved in:
Bibliographic Details
Published in:European journal of physics 2010-01, Vol.31 (1), p.101-114
Main Authors: Luaña, Víctor, Otero-de la Roza, A, Blanco, M A, Recio, J M
Format: Article
Language:English
Subjects:
Communication, education, history, and philosophy
Exact sciences and technology
General physics
Physics
Physics literature and publications
Surveys and tutorial papers, resource letters
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The particle-in-the-box, with or without an additional potential, is proposed as an excellent laboratory to teach and explore the details of the linear variational method using a non-orthogonal basis. The xn(a - x)n and xn(a/2 - x)(a - x)n polynomials are shown to form a complete basis for the even and odd states, respectively, of the particle confined to the x [0, a] interval. A short and simple Octave code is presented as the natural extension to the hand calculations when the basis set grows in size.
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/31/1/010