New state vector representation for the two-dimensional harmonic oscillator

차문회

Adam Miranowicz, Tomáš Opatrný, J. Bajer

DAVID J. ROWE

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

Jiaye Li

The paper first shows that the harmonic oscillator with quantum phase may provide a new way for quantization of field, then mainly studies the mathematicl characteristics of the harmonic oscillator with quantum phase, i.e., its representation theory. The representation in Fock space (being finite-dimensional) and two kinds of coherent states are discussed. It is shown that the statistical properties of the two kinds of coherent states are entirely different.

Le‐Man Kuang, Fa-Bo Wang, Yan-Guo Zhou

Xiao Liu

The author gives four approaches of calculating the energy eigenvalues of one dimensional harmonic oscillator.They are respectively the method of finding the solution in coorinate representation,the method of finding the solution in momentum representation;the method of finding the solution in energy representation,and the method of finding the solution by direct vectors.\;