2018/04/11 by Hong Zhang, Zhang, Hong
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.48550/arxiv.1804.04057
arxiv created 2018/04/11 · openalex publication_date 2018/04/11 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schrödinger equations for the free particle and the one in potential fields in heterogeneous complex media are found. The fractional equation of motion and the fractional virial theorem for anomalous quantum mechanics are then developed. Applying the fractional virial theorem, we derive an anomalous hydrogen atom whose transition energy values are much higher than that of Bohr hydrogen atom. The anomalous Heisenberg picture being equivalent to the fractional Schrödinger picture is also discussed.