A non-trivial PT-symmetric continuum Hamiltonian and its Eigenstates and Eigenvalues

• URL: http://arxiv.org/abs/2206.12900v2
• Date: Sat, 6 Aug 2022 02:03:30 GMT
• Title: A non-trivial PT-symmetric continuum Hamiltonian and its Eigenstates and Eigenvalues
• Authors: Lawrence Mead, David Garfinkle, Sungwook Lee
• Abstract summary: A non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set.
• Score: 1.2891210250935146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, a non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the simple harmonic oscillator. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set. We also find the hidden symmetry operator, ${\cal C}$, for this system. All calculations are performed analytically and without approximation.

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