On Quantum Tunneling Time In Uniform Gravitational Field

The concept of time is crucial to any fundamental theory. In the thesis,we will first sketch the historical changes in the notion of time in quantum mechanics,and then examine the role time plays in quantum theory.We especially focus on the tunneling time in quantum mechanics.The issue of tunneling time is replete with controversy.The controversy stems from the fact that first of all,the tunneling time has many different definitions,for example,the quantum phase time,dwell time etc.We discuss some of the important properties of the tunneling time in some barriers,and we prove some of the fundamental relations between them.Secondly, many tunneling time definitions seem to predict super-luminal tunneling velocities,which contract with the principle of Special relativity.This is so-called the Hartman Effect,which show that the tunneling time becomes independent of barrier length for thick enough barriers, ultimately resulting in unbounded tunneling velocities.There exists many experimental evidence shows apparent super-luminality,however,the physical explanation of the effect is still not clear to this day.What’s more,we also review the research on Hartman Effect and its recent development.