TITLE:
Atomic Quantum Mechanics Based on Atomic Functions
AUTHORS:
Sergei Yu. Eremenko
KEYWORDS:
Quantum Mechanics, Atomic Function, Atomic Wave Function, Atomic Oscillator, Atomic Spacetime, Unified Theories
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.11,
November
28,
2024
ABSTRACT: Based on theorems, the Atomic AString Functions theory, evolving since the 1970s, is introduced into Quantum Mechanics to represent a wave function via the shifts and stretches of smooth finite Atomic Function pulses/solitonic atoms. It leads to a novel ‘atomic interpretation’ where wave functions become the superpositions of localized Atomic Wave Functions, which can also describe collapsed wave functions, represent Gaussians, uphold Heisenberg’s uncertainly principle, and a more generic concept of Atomic Harmonic Oscillator. Atomic Functions can solve the boundary wave function discontinuity problem for particle-in-a-box and other solutions by introducing atomic wave packets. It highlights some limitations of the Schrödinger equation, yielding harmonic representations that may not be flexible enough to satisfy complex boundary conditions. The theory follows more generic research on Atomic Spacetime, quantum gravity, and field theories to derive common mathematical blocks of unified fields similar to loop quantum gravity and strings theories.