19,687 research outputs found
Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation
It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to
the raising and lowering operators derived from the factorization of radial
Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic
oscillator. It seems that there may exist intimate relation between the
closeness of classical orbits and the factorization of radial Schr\"{o}dinger
equation. Some discussion was made about the factorization of a 1D
Schr\"{o}dinger equation.Comment: 14 pages, no figure
Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor
We investigate the superconducting phase diagram and boundary modes for a
quasi-1D system formed by three Fe-Chains on an s-wave superconductor,
motivated by the recent Princeton experiment. The onsite
spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders
in the Fe-chains are shown to be crucial for the superconducting phases, which
can be topologically trivial or nontrivial in different parameter regimes. For
the topological regime a single Majorana and multiple Andreew bound modes are
obtained in the ends of the chain, while for the trivial phase only low-energy
Andreev bound states survive. Nontrivial symmetry reduction mechanism induced
by the term, diagonal hopping couplings, and magnetic
disorder is uncovered to interpret the present results. Our study also implies
that the zero-bias peak observed in the recent experiment may or may not
reflect the Majorana zero modes in the end of the Fe-chains.Comment: 5 pages, 4 figures; some minor errors are correcte
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