Quantum Many-Body Systems: Orthogonal Coordinates

M. C. Navarro, V.C Aguilera Navarro

Xiaoyan Gu, Bin Duan, Zhong-Qi Ma

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

T. K. Lim

An exact solution is obtained for a model three-body system in which the particles interact through pairwise, harmonic oscillator, and spin-dependent potentials, the solution being achieved by a simple transformation to an appropriate coordinate system. In particular, it is shown that the S-state wave functions of the ground state of the triton span the two-dimensional representation of the symmetric group S3, are orthogonal, and resemble closely the Irving wave forms found so successful in variational calculations.

Yoshio Kuramoto

Sun Shu-sheng

Using the transformation matrix between the unit basis vectors in deferent orthogonal curvilinear coordinate systems,we deduce the general form of the transformation between the angular momentum operators in these coordinate systems.We give the representations of Hamilton operator  and angular momentum operators in the orthogonal curvilinear coordinate system.We discuss the transformation matrix of unit basis vectors among the spherical coordinate system,cylindrical coordinates system and rectangular coordinates system,and the transformation between the angular momentum operators.Furthermore,we discuss the treatment of 2operator in different coordinate systems.