Abstract
In quantum mechanics , phase problem is an important issue , and has aroused fierce controversy in the 20th century . In the classical electrodynamics , the field strength is a basic physical quantity which describe the nature of electromagnetic field , and the vector potential is just a mathematical expression , but in quantum mechanics , the field strength can not describe the field completely , and the vector potential has important physical meanings . The discovery of AB effect beyond many people's expectations , so that people pay more attention to the laws of physics that hidden behind the quantum phase . Quantum mechanics has been applied in many aspects of modern technologies and promotes the development of quantum information science , it contains profound physical thinkings . This article uses vector potential as the basic point to discuss the formation of these effects such as AB effect , AC effect , Berry’s phase and Aharonov-Anadan phase and describes the process of experimental verifications of these effects , explains the differences between geometric phase of quantum mechanics and the phase which considered in traditional views . This article uses the two state system as the main example , analysis the geometric significance of Berry’s phase and its conditions on the parameters in this system , on the basis of these , comparing the differences between Berry’s phase and Aharonov-Anadan phase and the links between them , discussing the process of using quantum invariant to solve Berry’s phase .
Keywords: AB effect Berry's phase Aharonov-Anadan phase quantum invariant
experimental verifications
