2025/06/05 by E. E. Perepelkin, Б. И. Садовников, Perepelkin, E. E. +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2506.04725
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Previously we found a unique quantum system with a positive gauge-invariant Weyl-Stratonovich quasi-probability density function which can be defined by the so-called «quadratic funnel» potential [Phys. Rev. A 110 02222 (2024)]. In this work we have constructed a class of exact solutions to the 3D Schrödinger equation for a two-parameter «quadratic funnel» potential based on the -model of micro and macro systems. Explicit expressions for the energy spectrum and the set of eigenfunctions have been found. Using gauge invariance for scalar and vector potentials, a solution to the electromagnetic Schrödinger equation has been obtained, with a magnetic field in the form of a «Dirac string» defined by a singular vortex probability flux field. Superpositions of eigenfunctions leading to various types of vortex and potential probability current fields have been investigated in detail. The analysis of the quantum system's properties has been carried out within the Wigner-Vlasov formalism.