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- Title
Higher order quantum waves in fractal dimensions from nonlocal complex derivative operator.
- Authors
El-Nabulsi, Rami Ahmad; Anukool, Waranont
- 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.
- Subjects
FRACTAL dimensions; GROUND state energy; X-ray bursts; X-ray lasers; SCHRODINGER equation; POWER law (Mathematics); QUANTUM wells
- Publication
Canadian Journal of Physics, 2024, Vol 102, Issue 7, p375
- ISSN
0008-4204
- Publication type
Article
- DOI
10.1139/cjp-2024-0005