Quantum Systems Connected by a Time-Dependent Canonical Transformation

• Published in: Communications in theoretical physics 2009-09, Vol.52 (9), p.416-420, Article 416
• Main Authors: Yeon, Kyu Hwang, Choi, Jeong Ryeol, Shou, Zhang
• Format: Article
• Language: English
• Subjects: 保守系统; 哈密顿描述; 哈密顿系统; 时间依赖性; 正则变换; 相互联系; 量子系统
• ISSN: 0253-6102
• DOI: 10.1088/0253-6102/52/3/07

We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.