Original scientific paper

Supersymmetric algebra of the hydrogen atom and the tensor force

Josip Crnugelj ; Ruđer Bošković Institute, 41001 Zagreb, P. 0. B. 1016, Croatia, Yugoslavia
Mladen Martinis ; Ruđer Bošković Institute, 41001 Zagreb, P. 0. B. 1016, Croatia, Yugoslavia

Abstract

Using the factorization property of a three-dimensional hydrogen-atom-like Hamiltonian H(0), we generate a series of related Hamiltonians H(n) (n = 1, 2, 3) corresponding to a definite number of fermions, which are block diagonal components of an 8 x 8 matrix supersymmetric Hamiltonian. We find that H(0) (α) = H(3) (-α) and H(1) (α) = H(2) (-α), with α being the fine-structure constant. By introducing the „spin“ operator in the space of fermions, we show that the total angular momentum operators, Jk = Lk + Sk and S2, commute with the supersymmetric Hamiltonian and can be used to classify its eigenstates. We also show that the 3 x 3 matrix Hamiltonian H(1) (and similarly H(2)) can be written in the form which explicitly exhibits the structure corresponding to the tensor and spin-spin interaction between two spin-1/2 particles. The relative strength between the Coulomb tensor and the spin-spin interaction is fixed by supersymmetry.

Keywords

Hrčak ID:

331445

URI

https://hrcak.srce.hr/331445

Publication date:

5.7.1988.

Article data in other languages: croatian

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