| 1 Capabilities of Approximate Methods in Quantum Theory |
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1 | (26) |
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1.1 Effectiveness Criteria for Approximate Methods |
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2 | (4) |
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1.2 Perturbation Theory for Solution of Stationary Schrodinger Equation |
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6 | (7) |
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1.3 Non-perturbative Methods for Stationary Schrodinger Equation |
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13 | (11) |
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24 | (3) |
| 2 Basics of the Operator Method |
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27 | (54) |
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2.1 The Zeroth Approximation Choice |
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28 | (10) |
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2.2 Iteration Scheme for Calculation of the Successive Approximations |
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38 | (7) |
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2.3 Calculation Accuracy of the Wave Function |
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45 | (3) |
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2.4 Iterative Solution for Inverse Problem |
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48 | (3) |
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2.5 Non-perturbative Approach in the Theory of Classical Nonlinear Oscillations |
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51 | (8) |
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2.6 Why Do the OM Successive Approximations Converge? |
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59 | (6) |
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2.7 Calculation of Energy and Level Width of Quasi-Stationary States |
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65 | (7) |
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2.8 States with a Broken Symmetry (Integrals of Motion) |
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72 | (7) |
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79 | (2) |
| 3 Applications of OM for One-Dimensional Systems |
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81 | (48) |
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3.1 Anharmonic Oscillator with High Anharmonicity |
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82 | (6) |
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3.2 Anharmonic Oscillator with Non-symmetric Potential |
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88 | (4) |
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92 | (3) |
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3.4 Solution of the Mathieu Equation |
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95 | (8) |
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3.5 Quasienergies and Wave Functions of the Two-Level System in a Classical Monochromatic Field |
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103 | (6) |
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3.6 More Applications of Operator Method |
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109 | (8) |
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3.7 Operator Method for Uniformly Suitable Approximation of Integrals and Sums |
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117 | (10) |
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127 | (2) |
| 4 Operator Method for Quantum Statistics |
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129 | (58) |
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4.1 General Algorithm for Calculation of PF |
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129 | (4) |
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4.2 Statistics of Non-interacting Systems with One-Dimensional Energy Spectrum |
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133 | (27) |
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4.3 Coupled Quantum Anharmonic Oscillators (CQAO) |
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160 | (6) |
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166 | (10) |
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4.5 Calculation of Physical Characteristics |
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176 | (8) |
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184 | (3) |
| 5 Quantum Systems with Several Degrees of Freedom |
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187 | (28) |
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5.1 Analytical Approximation for the Energy Levels of CQAO |
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188 | (7) |
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5.2 Comparison with Known Analytical and Numerical Results |
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195 | (8) |
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5.3 Regular Perturbation Theory for Two-Electron Atoms |
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203 | (5) |
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5.4 Energies of the Excited States |
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208 | (5) |
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213 | (2) |
| 6 Two-Dimensional Exciton in Magnetic Field with Arbitrary Strength |
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215 | (36) |
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6.1 The Schrodinger Equation through the Levi-Civita Transformation |
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216 | (2) |
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6.2 Solving the Schrodinger Equation by the Operator Method |
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218 | (6) |
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6.3 Exact Numerical Solutions |
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224 | (5) |
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6.4 Schr6dinger Equation with Asymptotic Components |
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229 | (4) |
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6.5 Highly Accurate Analytical Solutions |
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233 | (8) |
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6.6 OM Application to Complex Two-Dimensional Atomic Systems |
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241 | (8) |
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249 | (2) |
| 7 Atoms in the External Electromagnetic Fields |
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251 | (36) |
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7.1 Hydrogen-Like Atom and Harmonic Oscillator |
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252 | (7) |
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7.2 Analytical Estimate for Rydberg States of a Hydrogen Atom in an Electric Field |
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259 | (5) |
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7.3 Iterative Calculation of Energy for Quasi-Stationary States |
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264 | (2) |
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7.4 Operator Method for Hydrogen Atom in Magnetic Field |
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266 | (5) |
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7.5 Two Level System in a Single-Mode Quantum Field |
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271 | (14) |
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285 | (2) |
| 8 Many-Electron Atoms |
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287 | (44) |
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8.1 Oscillator Model of Atom |
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289 | (5) |
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8.2 Continuous Oscillator Model in the Limit Z >> 1 |
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294 | (9) |
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8.3 Coulomb Based Atomic Model |
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303 | (20) |
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8.4 Effective Charges Model for Many-Electron Atom |
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323 | (6) |
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329 | (2) |
| 9 Systems with Infinite Number of Degrees of Freedom |
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331 | (28) |
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9.1 OM for Strong Coupling Polaron |
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332 | (8) |
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9.2 One-Dimensional Polaron |
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340 | (9) |
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9.3 UAA for Three-Dimensional Polaron Energy |
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349 | (6) |
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9.4 Particle-Field Interaction Model with a Divergent Perturbation Theory |
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355 | (2) |
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357 | (2) |
| Index |
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359 | |
Lisainfo e-raamatute kohta