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Variational Analysis of an Exactly Soluble Relativistic Oscillator

In: Symmetries in Science X

Author

Listed:
  • Marcos Moshinsky

    (UNAM, Instituto de Física)

  • Anju Sharma

    (UNAM, Instituto de Física)

Abstract

Variational methods in relativistic problems used basically atomic physics procedures, involving the properties of α and βmatrices, Slater or Sturm-Coulomb variational functions, etc. Recently the authors and their collaborators have developed methods for these problems more related to approaches used in non-relativistic nuclear physics. Instead of the 4×4 matrices αand βthey replaced them by direct products of 2×2 ones associated with ordinary and sign spins. The latter is mathematically identical with the isotopic spin, and thus the matrix representation of a relativistic Hamiltonian can be obtained in a simple fashion using harmonic oscillator basis states with the spins mentioned. In this paper the procedure indicated is applied to an exactly soluble relativistic oscillator Hamiltonian to show the effectiveness and quick convergence of the method. We also show clearly the separation of the positive and negative part of the energy spectrum, which allows us to compare the former with the exact energy levels.

Suggested Citation

  • Marcos Moshinsky & Anju Sharma, 1998. "Variational Analysis of an Exactly Soluble Relativistic Oscillator," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science X, pages 293-304, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1537-5_16
    DOI: 10.1007/978-1-4899-1537-5_16
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