Effect of Gravity in Quantum Mechanics

All possible theories of quantum gravity suggest the existence of a minimal length. Therefore, the usual Heisenberg uncertainty principle (HUP) is replaced by a more general uncertainty principle known as the generalized uncertainty principle (GUP). The dynamics of all quantum mechanical system gets modified due to GUP. In this work, we consider various quantum mechanical phenomena and review the correction to their respective Hamiltonian and energy levels. GUP modified quantization of a particle inside a box potential indicates that the space is quantized in the units of ($\alpha_0 l_p$), predicting an upper bound of the GUP parameter ($\alpha_0$). Furthermore, the modified Landau levels, simple harmonic oscillator (SHO) and Lamb shift also results in an upper bound of the GUP parameter. Apart from these, we review a relativistic quantum mechanical phenomenon, Dirac oscillator under the effect of magnetic field which is non-oscillating at a certain value of magnetic field even under the effect of gravity.

Banaras Hindu University