3
$\begingroup$

The Runge-Lenz operator enables an algebraic solution of Coulomb potential energy levels without a solution of a differential equation. What is the analog for the solution of the Dirac equation in a Coulomb potential and the associated energy levels. Is it possible to get the energy levels solely by algebraic methods and not solving the coupled differential equations. I have seen separation into angular and radial parts by algebraic means, but the radial equation always seems to be solved via the usual power series methods. Can this be avoided by using an analog of the Runge-Lenz operator for the Dirac equation?

$\endgroup$
1
  • $\begingroup$ From akhmeteli: L I Komarov and T S Romanova 1985 J. Phys. B: At. Mol. Phys. 18 859 The algebraic method of solution of the Dirac equation for a particle in a Coulomb potential. Abstract:An equation is constructed in two-dimensional complex space, in the set of solutions of which solutions of the Dirac equation for a particle in a Coulomb potential are present. These solutions are found by a purely algebraic method. I have not seen the article though. $\endgroup$
    – stafusa
    Jun 17 '18 at 11:16
1
$\begingroup$

L I Komarov and T S Romanova 1985 J. Phys. B: At. Mol. Phys. 18 859 The algebraic method of solution of the Dirac equation for a particle in a Coulomb potential

Abstract:An equation is constructed in two-dimensional complex space, in the set of solutions of which solutions of the Dirac equation for a particle in a Coulomb potential are present. These solutions are found by a purely algebraic method.

I have not seen the article though.

$\endgroup$
11
  • 2
    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ Jun 16 '18 at 22:37
  • $\begingroup$ @sammygerbil : I don't quite get it: there is no link in my answer, just a reference to a paper article. How can it change? And I provided the abstract. $\endgroup$
    – akhmeteli
    Jun 17 '18 at 1:02
  • 2
    $\begingroup$ In short, your answer is "Yes, read this article". You could have provided some details of the method, whether it uses an analog of the Runge-Lenz operator, explained how the two problems differ. $\endgroup$ Jun 17 '18 at 3:10
  • 2
    $\begingroup$ No, but they should provide some context for the link and be more informative than just saying Yes or No with a link or reference. This answer only repeats the question and says "Yes, the answer is in this article." The issue isn't that the link could be broken, but that the details are "in another castle". See Meta questions : meta.stackexchange.com/questions/110165/… and meta.stackexchange.com/questions/225370/… $\endgroup$ Jun 17 '18 at 3:56
  • 2
    $\begingroup$ Link-only answers also "get the asker going in the right direction", so there is some conflict here. As the script says, "While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference." I did not write the script. This is the site's standard not mine. $\endgroup$ Jun 17 '18 at 9:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.