Regensburg 2025 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster: Quantum Dynamics and Many-body Systems
DY 29.9: Poster
Wednesday, March 19, 2025, 15:00–18:00, P4
Subordination approach for derivation of generalized quantum models in non-relativistic and relativistic cases — •Irina Petreska1, Trifce Sandev1,2,3, and Alexander Iomin4,5 — 1Ss. Cyril and Methodius University in Skopje, Macedonia — 2Macedonian Academy of Sciences and Arts, Skopje, Macedonia — 3Korea University, Seoul, Korea — 4Solid State Institute, Technion, Haifa, Israel — 5Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
The generalized Schrödinger equation and the generalized Klein-Gordon equation are derived by applying the subordination approach to conventional quantum mechanics. The special cases of the fractional Schrödinger equation and the fractional Klein-Gordon equation are adequately introduced. Additionally, the subordination approach is also applied to derive the special case of the generalized Dirac equation for spin 1/2 particles and the directions for future research are discussed. It is evident that according to the subordination approach, the time fractional derivatives in quantum mechanics, including the relativistic one, can be related to the Lévy stable processes in time.
- T. Sandev, I. Petreska, A. Iomin, From standard to generalized Schrödinger and Klein-Gordon equations: Subordination approach, submitted (2024).
Keywords: Subordination approach; Generalized Schrödinger equation; Generalized Klein-Gordon equation; Fractional calculus; Mittag-Leffler function