The Shape Complexity of a Particle in the Circular Quantum Well with Homogeneous Perpendicular Magnetic Field

Abstract

The shape complexity of a particle confined in the circular quantum well with an external homogeneous perpendicular magnetic field is investigated. First, the Shannon entropy and the averaging electron probability density, as well as the shape complexities in the position and momentum spaces for several quantum states, are computed and discussed. The quantum confinement effect on the shape complexity of this system is extensively explored. Then, the influence of the magnetic field on the shape complexities of the particle confined in the circular quantum well is discussed. It is demonstrated that the shape complexity exhibits scaled invariance under the influence of the magnetic field. However, when the radius of the quantum well is fixed, the shape complexity of the given quantum state changes with the magnetic field strength. Results suggest that the shape complexity of a particle confined in the quantum well can be changed by varying both the strength of the magnetic field and the size of the well. This study has some practical applications in quantum information measurement of the confined particle and can guide future researches for the disorder characteristics of confined particle in semiconductor quantum dots.