NEW FEATURES OF SIMPLE QUANTUM SYSTEMS DUE TO GRAVITY VIA GENERALIZED UNCERTAINTY RELATION

The introduction of gravity has brought many interesting properties to quantum mechanics. States that give the lower limit of the uncertainty relation without gravity may change under the perturbation of gravity. Studying these peculiar properties using simple physical systems (such as a one-dimensional infinite deep potential well and a one-dimensional harmonic oscillator) can expand our understanding of quantum mechanics and appreciate the physical effects brought by gravity. In this paper, we introduce the generalized uncertainty relation into the one-dimensional infinite deep potential well and the one-dimensional harmonic oscillator, considering gravity as a perturbation potential field, and calculates the changes in the system's energy eigenvalues and eigenstates under perturbation, demonstrating the strange effects caused by gravity. The results indicate that under the first-order approximation, the energy eigenvalues do not change after considering the influence of gravity, but the energy eigenstates change. We also calculated the correction of gravity to the Virial theorem and presented the impact of the gravitational correction on the Virial theorem.