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Two simple models derived from a quantum-mechanical particle on an elliptical path
arXiv
Authors: Francisco M. Fernández
Year
2025
Paper ID
15883
Status
Preprint
Abstract Read
~2 min
Abstract Words
96
Citations
N/A
Abstract
We analyze two simple models derived from a quantum-mechanical particle on an elliptical path. The first Hamiltonian operator is non-Hermitian but isomorphic to an Hermitian operator. It appears to exhibit the same two-fold degeneracy as the particle on a circular path. More precisely, En=n2E1,\ n=1,2,ldots in addition to an exact eigenvalue $E0=0$. The second Hamiltonian operator is Hermitian and does not exhibit such degeneracy. In this case the nth excited energy level splits at the nth order of perturbation theory. Both models can be described in terms of the same point-group symmetry.
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- We analyze two simple models derived from a quantum-mechanical particle on an elliptical path.
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