ABSTRACT
Abstract ................................................................................................. 164 3.1 Introduction .................................................................................. 165 3.2 The Wave-Function Continuity .................................................... 169 3.2.1 Quantum Tunneling and the Gamow Factor .................... 169 3.2.2 Nuclear Systems’ Lifetime by Alfa Disintegration .......... 176 3.3 Eigen-Energies and Eigen-Functions ........................................... 181 3.3.1 Atomic Hydrogenic States by Solving
Laguerre Type Equations ................................................. 182 3.3.2 Molecular Vibrational States by Solving
Hermite Type Equations .................................................. 200 3.3.3 Solid State Free Electronic States .................................... 209 3.4 Semiclassical Quantification of Energy ....................................... 216 3.4.1 Hydrogenic Atomic Systems ........................................... 219 3.4.2 Molecular Vibrational Systems ........................................ 222 3.4.3 Generalized |x|α Potential Systems ................................... 223 3.5 Variational Wave-Function and Energies ..................................... 228 3.5.1 Hydrogen’s Quantum Ground Level ................................ 228 3.5.2 Vibrational Ground Level ................................................ 231 3.5.3 Ground State Paradox of Free Electrons in Solids .......... 232
3.6 Causal Quantum Evolution .......................................................... 236 3.6.1 Schrödinger’s Picture ....................................................... 236 3.6.2 Unitary (“U”) Picture. Heisenberg Picture ...................... 246 3.6.3 Quantum Transitions: Interaction Picture ........................ 254 3.6.4 Green Function and Its Causal Properties ........................ 262 3.6.5 Free Particle’s Propagator ................................................ 271 3.7 Stationary Perturbations ............................................................... 274 3.7.1 General Perturbation Algorithm ....................................... 275 3.7.2 The Zeeman Effect ........................................................... 281 3.7.3 Nuclear Isotropic Corrections on Hydrogenic Atoms ...... 285 3.7.4 Harmonic Oscillator Perturbations .................................. 292 3.7.5 Quasi-Free Electronic Model of Solids ........................... 300 3.8 Quantum Measurements .............................................................. 304 3.8.1 Classical vs. Quantum Electric Resistance ...................... 306 3.8.2 Quantum Conservation Laws ............................................311 3.8.3 Quantum Elastic Scattering on Fixed Target ................... 318 3.8.4 More about Scattering: Born Approximation
and Resonance Profile ..................................................... 332 3.8.5 From Yukawa Potential to Rutherford Scattering ............ 342 3.9 Conclusion ................................................................................... 353 Keywords .............................................................................................. 354 References ............................................................................................. 355 Author’s Main References ........................................................... 355 Specific References ...................................................................... 355 Further Readings .......................................................................... 355
ABSTRACT
The phenomenological quantum mechanics is practically “re-storied” in a more formalized way, under the so-called extended quantum postulates, while opening and unfolding more complex analysis of the Nature’s phenomena, from nuclear, to atomic, to molecular, and to solid state and scattering observational quantum effects.
