Power Law Duality in Classical and Quantum Mechanics
| Autor: | Georg Junker, Akira Inomata |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Physics and Astronomy (miscellaneous) General Mathematics quark confinement Physics - History and Philosophy of Physics FOS: Physical sciences Duality (optimization) Semiclassical physics Physics - Classical Physics 02 engineering and technology 01 natural sciences Schrödinger equation Quantization (physics) symbols.namesake Quantum mechanics 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) History and Philosophy of Physics (physics.hist-ph) ddc:530 Supersymmetric quantum mechanics acoustics Mathematical Physics Physics supersymmetric quantum mechanics Quantum Physics 010308 nuclear & particles physics semiclassical quantization lcsh:Mathematics classical and quantum mechanics Classical Physics (physics.class-ph) Mathematical Physics (math-ph) lcsh:QA1-939 Action (physics) Symmetry (physics) Dual (category theory) High Energy Physics - Theory (hep-th) Chemistry (miscellaneous) power-law duality symbols 020201 artificial intelligence & image processing Quantum Physics (quant-ph) |
| Zdroj: | Symmetry, Vol 13, Iss 409, p 409 (2021) Symmetry Volume 13 Issue 3 |
| ISSN: | 2073-8994 |
| Popis: | The Newton--Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton's characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of {the} Green function satisfying the radial Schr\"odinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb--Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential. Comment: 57 pages, 2 figures |
| Databáze: | OpenAIRE |
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