Lad, Vivek
College of Science and Mathematics
Professor: Dr. Gardo Blado
ABSTRACT:
For the last fifty years physicists have been attempting to unify two main areas of physics: quantum mechanics and gravity. This theory of quantum gravity currently has two workable approaches: loop quantum gravity (LQG) and string theory (ST). Both LQG and ST predict a minimal length which is on the order of the Planck length, which changes the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle (GUP). As a result we have a modified Schrodinger Equation through which we can observe how quantum gravity will affect classic examples in quantum mechanics such the particle in a box, the finite potential well, and the quantum harmonic oscillator. Another common example in quantum mechanics is alpha decay. Alpha decay is a form of radioactive process in which an atomic nucleus emits an alpha particle consisting of two protons and two neutrons. This alpha particle is approximated to be trapped in some arbitrarily shaped potential well and prevented from escaping due to a Coulomb barrier. However, an alpha particle may escape from the atomic nucleus by “tunneling” its way through the potential barrier, even though the energy of the particle is less than that of the barrier. It is the goal of this research to see how a quantum-gravity induced minimal length (via the Generalized Uncertainty Principle) will affect alpha decay rates.
