Study on Rényi Entropy, Tsallis Entropy, and Onicescu Information Energy of a Particle in a Quantum Well with a Uniform Electric Field

The study of quantum information entropy in confined quantum systems plays a pivotal role in quantum information science. In this work, we investigate the quantum information entropy of a particle in a quantum well under an external electric field by calculating the Rényi entropy (), Tsallis entropy () and the Onicescu information energy (). Our findings reveal that these entropic measures exhibit a strong dependence on the entropy order ( α ). Although both and demonstrate a decreasing trend with increasing α for any given quantum state, they differ significantly in their sensitivity to α variations, displaying distinct behaviors that provide unique insights into quantum uncertainty. For the Onicescu information energy (), a sharp transition around α = 1 appears. This characteristic could be significant for designing and analyzing quantum systems, particularly in enhancing their information processing capabilities. By further examining how these entropic measures vary with quantum well width and electric field strength, we gain a deeper understanding of the system's controllability. This empowers researchers to select optimal metrics for specific applications and improve the accuracy of quantum analyses. This study underscores the importance of entropy‐based analysis in quantum mechanics for advancing quantum control, information theory, and technology development.