| INTRODUCTION | 4 | ||
| GENERAL CHARACTERIZATION OF THE THESIS | 5 | ||
| CHAPTER 1 MULTILEVEL MODELS OF MULTIPHOTON VIBRATIONAL EXCITATION OF MOLECULES (REVIEW) | 9 | ||
| 1.1. | Phenomenon of multiphoton excitation of molecules and multilevel systems | 9 | |
| 1.2. | Methods to solve equations of coherent dynamics for systems of levels | 14 | |
| 1.3. | Orthogonal polynomials and method to obtain analytic solutions for multilevel systems | 19 | |
| CHAPTER 2 MULTILEVEL QUANTUM SYSTEMS AND CHRISTOFFEL-LEGENDRE ORTHOGONAL POLYNOMIALS | 21 | ||
| 2.1. | Christoffel formula | 21 | |
| 2.2. | Non-equidistant disposition of levels. Excitation of Christoffel-Legendre-1 systems | 23 | |
| 2.3. | Models with equidistant levels. Resonant excitation of Christoffel-Legendre-2 systems |
30 | |
| 2.4. | Two-parameter family of models with equidistant
levels. Peculiarities of dynamics of Christoffel-Legendre-4 systems |
35 | |
| 2.5. | Comparison of characteristics of different quantum systems | 41 | |
| CHAPTER 3 QUANTUM SYSTEMS WHICH ARE DESCRIBED WITH AID OF UVAROV-LEGENDRE POLYNOMIALS | 51 | ||
| 3.1. | Christoffel-Uvarov formula | 51 | |
| 3.2. | Uvarov-Legendre-1 systems
with non-equidistant levels. Models with great frequency detunings on lower transitions |
54 | |
| 3.3. | Uvarov-Legendre-1 systems
with equidistant levels. Peculiarities of dynamics at low value of didole moment on second transition |
62 | |
| 3.4. | Multilevel quantum systems which are described with aid of polynomials with inverse weight functions | 69 | |
| CHAPTER 4 MULTILEVEL SYSTEMS AND ORTHOGONAL FUNCTIONS | 75 | ||
| 4.1. | Generalization of the analytic method | 75 | |
| 4.2. | Resonant excitation of
N-level equidistant systems. Models with rapidly increasing or decreasing dependence of dipole moment of transitions on level number |
80 | |
| 4.3. | Models with non-equidistant energy spectrum. Dynamics of non-closed multilevel systems |
100 | |
| CONCLUSIONS | 123 | ||
| LIST OF REFERENCES | 124 |