56 citations · 120 across the 7 of their papers we have counts for
7 papers
Can the canonical quantization be accomplished within the intrinsic geometry?
D. M. Xun, Q. H. Liu
For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that…
On relation between geometric momentum and annihilation operators on a two-dimensional sphere
Q. H. Liu, Y. Shen, D. M. Xun +1
With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihi…
Quantum motion on a torus as a submanifold problem in a generalized Dirac's theory of second-class constraints
D. M. Xun, Q. H. Liu, X. M. Zhu
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted b…
Geometric momentum in the Monge parametrization of two dimensional sphere
D. M. Xun, Q. H. Liu
A two dimensional surface can be considered as three dimensional shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on…
Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
Q. H. Liu, L. H. Tang, D. M. Xun
In Dirac's canonical quantization theory on systems with second-class constraints, the commutators between the position, momentum and Hamiltonian form a set of algebraic relations…
A simple realization of gl(2,c) Lie algebra with vector operators on sphere
Q. H. Liu, X. P. Rong, D. M. Xun
By utilization of three elementary vector operators as position, angular momentum and their cross product, a simple realization of gl(2,c) Lie algebra on sphere are constructed. Th…
Raising and lowering operators for angular momentum quantum numbers l in spherical harmonics
Q. H. Liu, D. M. Xun, L. Shan
Two vector operators aimed at shifting angular momentum quantum number l in spherical harmonics |lm>, primarily proposed by Prof. X. L. Ka in 2001, are further studied. For a given…