{"title":"Higher order quantum waves in fractal dimensions from nonlocal complex derivative operator","authors":"R. El-Nabulsi, Waranont Anukool","doi":"10.1139/cjp-2024-0005","DOIUrl":null,"url":null,"abstract":"In this study, we introduced a new nonlocal complex derivative operator in fractal dimension based concurrently on the concept of “nonlocal generalized complex backward-forward coordinates” and the “product-like fractal measure”. The quantization of the theory in fractal dimension leads to a higher order Schrödinger equation characterized by a higher order energy operator. As an illustration, we have discussed the cases of infinite quantum well and power-law potentials. Their associated zero-point energies were found to depend on the numerical value of the fractal dimension. For the infinite well, the decrease in zero-point energy with fractal dimension may result in the emission of large wavelengths photons observed experimentally in X-ray laser bursts emitted from the solid.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2024-0005","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we introduced a new nonlocal complex derivative operator in fractal dimension based concurrently on the concept of “nonlocal generalized complex backward-forward coordinates” and the “product-like fractal measure”. The quantization of the theory in fractal dimension leads to a higher order Schrödinger equation characterized by a higher order energy operator. As an illustration, we have discussed the cases of infinite quantum well and power-law potentials. Their associated zero-point energies were found to depend on the numerical value of the fractal dimension. For the infinite well, the decrease in zero-point energy with fractal dimension may result in the emission of large wavelengths photons observed experimentally in X-ray laser bursts emitted from the solid.
期刊介绍:
The Canadian Journal of Physics publishes research articles, rapid communications, and review articles that report significant advances in research in physics, including atomic and molecular physics; condensed matter; elementary particles and fields; nuclear physics; gases, fluid dynamics, and plasmas; electromagnetism and optics; mathematical physics; interdisciplinary, classical, and applied physics; relativity and cosmology; physics education research; statistical mechanics and thermodynamics; quantum physics and quantum computing; gravitation and string theory; biophysics; aeronomy and space physics; and astrophysics.