2017/04/12 by Andrei Galiautdinov, Galiautdinov, Andrei
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1704.03825
openalex publication_date 2017/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate a simple condition for reconstructibility of a certain class of Hamiltonians with real potentials from the knowledge of their complex-valued eigenfunctions. This may be relevant to the question of preparability of quantum states raised by W. Lamb in his 1969 paper on operational interpretation of quantum mechanics. Of particular interest to engineering applications are: (a) an exotic case of an upside-down harmonic-oscillator-type potential (a variation of the inverted "Mexican hat" potential) whose square-integrable complex eigenfunction describes a localized scattering state similar to the "bound state in the continuum" of von Neumann and Wigner, and (b) a spatially confined scattering state of a particle moving in an infinite well with the properly shaped potential bottom.