Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions. (13th February 2013)

• Record Type: Journal Article
• Authors: Hall, Richard L.; Rodríguez, Alexandra Lemus
• Other Names: Pelinovsky D. E. Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2013(2013)
• Publication Date: 2013-02-13
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2013/258203
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : It is shown that the spanning set forL 2 ( [ 0, 1 ] ) provided by the eigenfunctions{ 2 sin ( n π x ) } n = 1 ∞ of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems. The basis is scaled to[ a, b ], wherea andb are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box inR d turns out to be appropriate also for problems that are softly confined by U -shaped potentials, including those with strong singularities atr = 0 . Specific examples are discussed in detail, along with some boundN -boson systems.