PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential

Abstract

Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in general. Some aspects of the spontaneous breakdown of PT symmetry are analysed.

16 pages; to appear in Phys. lett. A

References in corpus (7)

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• Space of State Vectors in PT Symmetrical Quantum Mechanics
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
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• Poeschl-Teller paradoxes

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• Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• An exactly solvable PT symmetric potential from the Natanzon class
• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• PT-symmetry and its spontaneous breakdown explained by anti-linearity
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Remarks on PT-pseudo-norm in PT-symmetric quantum mechanics
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• Linear representation of energy-dependent Hamiltonians
• A new solvable complex PT-symmetric potential
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Analytical solutions for the radial Scarf II potential
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• An ansatz for the eigenstates in PT-symmetric quantum mechanics
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $\ell$-Values