Time-dependent quantum mechanics in particle and nuclear physics

K. Heyde, John L. Wood

This book, the first of a two-volume set, provides a comprehensive introduction to quantum mechanics for advanced undergraduate and postgraduate students entering the field of nuclear structure studies via two-state systems: both polarized photons and spin-1/2 particles. This leads to the logic behind the physical structure and an axiomatic formulation using linear spaces and operators. The one-dimensional harmonic oscillator is used to illustrate the mechanics of quantized systems, reaching to time dependence and coherent states. Measurement theory is introduced. The transformation theory of space and time leads to wave functions. The role of group theory and rotations then leads to the quantization of angular momentum. Central force problems are handled algebraically. The development is completed with quantization of motion of a charged particle in a magnetic field. Part of IOP Series in Nuclear Spectroscopy and Nuclear Structure.

M. Corcoran

Contents Light Wave Mechanics The Time-Independent Schrodinger Equation One-Dimensional Potentials Principles of Quantum Mechanics Quantum Mechanics in three Dimensions Identical Particles Solid-State Physics Nuclear Physics Particle Physics Appendix i: Special Relativity Appendix ii: Power-Series Solutions Appendix iii: Constants and Conversion Factors

Zoltán Papp

A. Obertelli, Hiroyuki Sagawa

Alexey Gromov

Abstract A hypothesis is proposed according to which the sole difference between the quantum and classical worlds is the time scale. A quantitative verification of the model has been carried out on systems ranging from atomic to macroscopic scales. The concept of a temporal wake is introduced — a physical field generated by the motion of a particle in its ultrafast proper time. It is shown that this approach not only explains key quantum phenomena (interference, entanglement, tunneling) but also connects them with gravity. Based on the hypothesis, a phenomenological toy model is constructed, demonstrating quantitative agreement with experimental data. Three laws of scale invariance are formulated. A system of coupled field equations is proposed in which the coupling between particles is realized through an effective parameter αeff depending on the time scale, system symmetry, and density. It is found that αeff naturally describes a phase transition between atomic, nuclear, and classical regimes. Testable predictions are formulated, including an experiment on wake shielding (Prediction I) and the search for a phase transition at nuclear density (Prediction L).