Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots

The virial theorem is a fundamental principle giving the relationship between kinetic and potential energies in classical and quantum mechanical systems. In this study, the virial theorem was investigated using the scaling method in quantum dot structures. Two different approaches were used; the wave function of the position vector was scaled only in the first approach, while the dot radius was scaled only in the second approach. This method is valid not only for single-electron systems but can also be applied to multi-electron systems. In the calculations, the virial theorem was satisfied. Furthermore, the average energy of the system was minimized, and so on demonstrating that this approach provides a highly accurate and stable framework for multi-electron systems.