7 papers
Critique of Breit-Wigner resonance scattering
Philip D. Mannheim
In the standard Breit-Wigner approach to scattering the phase shift is to have a form at a real energy resonance. This leads to complex energy poles…
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…
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…
Creating a Universe from Nothing as an Alternative to the Cosmological Principle
Philip D. Mannheim, Daniel A. Norman, Tianye Liu
In the cosmological Robertson-Walker geometry required of the cosmological principle both the Weyl tensor and the Bach tensor $W^{μν}=[2\nabla_κ\nabla_λ-R_{λκ}…
Properties of associated Legendre conical functions
Daniel A. Norman, Philip D. Mannheim, Tianye Liu
We present some new properties of associated Legendre conical functions of the first and second kind, and . In particular w…
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…