Quantum mechanics with difference operators
作者： R Twarock , V.K Dobrev , H.-D Doebner
DOI: 10.1016/S0034-4877(02)80069-6
关键词: Constant coefficients 、 Operator algebra 、 Spectral theorem 、 Fourier integral operator 、 Mathematics 、 Operator theory 、 Witt algebra 、 Creation and annihilation operators 、 Quantum mechanics 、 Multiplicative function
摘要: A formulation of quantum mechanics with additive and multiplicative (q-) difference operators instead differential is studied from first principles. Borel-quantisation on smooth configuration spaces used as guiding quantisation method. After a short discussion this method translated step-by-step to framework based operators. To restrict the resulting plethora possible quantisations additional assumptions motivated by simplicity plausibility are required. Multiplicative corresponding q-Borel kinematics given circle its N-point discretisation; connection q-deformations Witt algebra discussed. For “natural” choice q-kinematics q-difference evolution equation obtained. This study shows general difficulties for generalisation physical theory known one “new” framework.
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