| 摘要 | 第1-9页 |
| Abstract | 第9-13页 |
| Contents | 第13-16页 |
| 1 Introduction | 第16-34页 |
| ·Solvable systems and their dynamical symmetries | 第16-28页 |
| ·Virial Theorem, Hypervirial Theorem and Hellmann-Feynman Theorem | 第28-30页 |
| ·Results in this thesis | 第30-34页 |
| 2 Virial Theorem for a class of quantum nonlinear harmonic oscil-lators | 第34-40页 |
| ·Introduction | 第34-35页 |
| ·Virial Theorem for Carinena's QNHO | 第35-37页 |
| ·Virial Theorem for the general class of exactly solvable QNHO | 第37-38页 |
| ·Conclusion | 第38-40页 |
| 3 Virial Theorem and Hypervirial Theorem in a spherical geome-try | 第40-56页 |
| ·Introduction | 第40-43页 |
| ·Virial Theorem | 第43-47页 |
| ·Hypervirial Theorems | 第47-49页 |
| ·Application of The Hypervirial Theorems | 第49-53页 |
| ·Conclusion | 第53-56页 |
| 4 Higgs algebraic symmetry of screened system in a spherical ge-ometry | 第56-64页 |
| ·Introduction | 第56-59页 |
| ·Screened Coulomb potential | 第59-62页 |
| ·Screened isotropic harmonic oscillator | 第62-63页 |
| ·Conclusion | 第63-64页 |
| 5 Constructing the quantum systems with dynamical symmetry | 第64-80页 |
| ·Introduction | 第64-66页 |
| ·Constructing approach | 第66-68页 |
| ·Coulomb-like system | 第68-72页 |
| ·Oscillator-like system | 第72-75页 |
| ·Non-central potential system | 第75-77页 |
| ·Conclusion | 第77-80页 |
| 6 Conclusion | 第80-88页 |
| ·Virial Theorem for quantum nonlinear harmonic oscillators | 第81-82页 |
| ·Virial Theorem and Hypervirial Theorem in a spherical geometry | 第82-84页 |
| ·Higgs algebraic symmetry of screened system in a spherical geometry | 第84-85页 |
| ·Constructing the quantum systems with dynamical symmetry | 第85-88页 |
| Biblography | 第88-94页 |
| 致谢 | 第94-96页 |
| 个人简介 | 第96-97页 |
