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quant-ph2026
PT symmetry and the square well potential: Antilinear symmetry rather than Hermiticity in scattering processes
Philip D. Mannheim
A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being…
quant-ph2026
States that grow linearly in time, exceptional points, and zero norm states in the simple harmonic oscillator
Philip D. Mannheim
The simple harmonic oscillator has a well-known normalizable, positive energy, bound state spectrum. We show that degenerate with each such positive energy eigenvalue there is a no…
quant-ph2025
Time Advance and Probability Conservation in PT-Symmetric Quantum Mechanics
Philip D. Mannheim
When excited states decay the time evolution operator does not obey . Nonetheless, probability conservation is not lost if one includes both e…