Lagrange-multiplier regularization of eigenproblem for Jx

KPOPℰ Collaboration

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We solve the eigenproblem of the angular momentum Jx by directly dealing with the non-diagonal matrix unlike the conventional approach rotating the trivial eigenstates of Jz. Characteristic matrix is reduced into a tri-diagonal form following Narducci–Orszag rescaling of the eigenvectors. A systematic reduction formalism with recurrence relations for determinants of any dimension greatly simplifies the computation of tri-diagonal matrices. Thus the secular determinant is intrinsically factorized to find the eigenvalues immediately. The reduction formalism is employed to find the adjugate of the characteristic matrix. Improving the recently introduced Lagrange-multiplier regularization, we identify that every column of that adjugate matrix is indeed the eigenvector. It is remarkable that the approach presented in this work is completely new and unique in that any information of Jz is not required and only algebraic operations are involved. Collapsing of the large amount of determinant calculation with the recurrence relation has a wide variety of applications to other tri-diagonal matrices appearing in various fields. This new formalism should be pedagogically useful for treating the angular momentum problem that is central to quantum mechanics course.

Original languageEnglish
Pages (from-to)1089-1103
Number of pages15
JournalJournal of the Korean Physical Society
Issue number12
Publication statusPublished - 2021 Dec


  • Angular momentum
  • Eigenvalue problem
  • Lagrange multiplier
  • Quantum mechanics

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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