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Pseudospin symmetry in supersymmetric quantum mechanics: Schr\"odinger equations
The origin of pseudospin symmetry (PSS) and its breaking mechanism are
explored by combining supersymmetry (SUSY) quantum mechanics, perturbation
theory, and the similarity renormalization group (SRG) method. The
Schr\"odinger equation is taken as an example, corresponding to the
lowest-order approximation in transforming a Dirac equation into a diagonal
form by using the SRG. It is shown that while the spin-symmetry-conserving term
appears in the single-particle Hamiltonian , the PSS-conserving term appears
naturally in its SUSY partner Hamiltonian . The eigenstates of
Hamiltonians and are exactly one-to-one identical except for
the so-called intruder states. In such a way, the origin of PSS deeply hidden
in can be traced in its SUSY partner Hamiltonian . The
perturbative nature of PSS in the present potential without spin-orbit term is
demonstrated by the perturbation calculations, and the PSS-breaking term can be
regarded as a very small perturbation on the exact PSS limits. A general
tendency that the pseudospin-orbit splittings become smaller with increasing
single-particle energies can also be interpreted in an explicit way.Comment: 31 pages, 11 figures, 2 table
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