Document Type

Article

Publication Date

1991

Publication Title

Journal of Physics A: Mathematical and General

Volume

24

Issue

1

First Page

79

Last Page

94

Abstract

In this and the following two papers in this series it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The angular part of such calculations, being well understood, is performed in the standard way. In this, the first paper, it is shown how a suitable linear transformation of the two relativistic radial wavefunctions allows the pair of relativistic coupled differential equations to be written as two uncoupled second-order equations which are simple generalizations of the corresponding non-relativistic equation. This transformation is presented in a manner which allows for a simple extension to the Green function problem. The transformed relativistic wavefunctions are explicitly derived and the normalization is presented in a novel and simple way. A new derivation is given for the recursion relations for both non-relativistic and relativistic radial wavefunctions, some of which are new. These relations are required in the subsequent papers.

Comments

This article is Copyright Institute of Physics (the "Institute") and IOP Publishing 2010. References to "IOP" mean the Institute and/or IOP Publishing, as appropriate. References to "this website" are to the IOP website from which the user is linking to this Copyright Notice - http://iopscience.iop.org/ Please read the following Copyright Notice carefully as your access to and use of this website will be deemed as acceptance of its terms. This Copyright Notice was last updated on 30 December 2009. The material featured on this website is subject to IOP copyright protection, unless otherwise indicated. Subject to subscriber status, reasonable amounts of IOP copyright-protected material (other than logos) may be reproduced, distributed or communicated to others free of charge in any format or media for the purposes of research for a non commercial purpose, or for private study, or for internal circulation within an organization. This is subject to the material being reproduced accurately and not being used in a misleading context. Where any IOP copyright items on this website are being reproduced, distributed or communicated to others, the source of the material must be identified and the copyright status acknowledged. In particular, where a third party wishes to include IOP copyright items on another website, they must only use non-locked-down content, link to the home-page of this website rather than reproducing the items, and fully credit this website and the copyright status of the item. Any other proposed use of IOP material will be subject to a copyright licence, available from IOP. Systematic downloading of files is prohibited. The permission to reproduce, distribute or communicate IOP-protected material does not extend to anything that is identified as being the copyright of a third party. Authorization to reproduce, distribute or communicate such material must be obtained from the copyright owner concerned. In addition, the names, images and logos identifying IOP are proprietary marks of IOP or its licensors. Other names, images and logos identifying third parties and their information, products and services are the proprietary marks of third parties. Copying or using IOP's logos and/or any third party logos accessed via this website is not permitted without the prior written approval of the relevant trade mark and/or copyright owner.

Download

Included in

Physics Commons

Share

COinS