Quantum mechanics presented as harmonic analysis

Jincheng Zhang

This paper explores the mathematical framework for analyzing the collapse of quantum states, extending the concept of harmonic analysis to quantum systems. We propose a novel non-linear harmonic operator that describes the evolution of the system's energy and phase as it approaches the state of collapse. This operator allows for the prediction of specific outcomes, offering a rigorous and mathematically grounded approach to understanding quantum phenomena. The core mechanism involves introducing a dynamically evolving operator that captures the intricate interplay between quantum mechanics and the concept of collapse. We demonstrate the framework's efficacy through simulations and theoretical analysis, highlighting its potential to provide a more precise understanding of quantum state dynamics.

Shuji Watanabe

<p>Sihui Yan¹, Jie Huang²</p>

Quantum mechanics holds a very important position as the theoretical foundation of the micro world. Harmonic oscillator system is a very classical model in quantum mechanics. In this paper, the wave function of a three-dimensional linear harmonic oscillator is derived based on the linear harmonic oscillator model in quantum mechanics. According to the probabilistic interpretation of quantum mechanics, we obtain the probability density function of the harmonic oscillator electron cloud. In this paper, Monte Carlo selection method is used for sampling, and Mathematica software is used to draw electron cloud images with different quantum number, so that people can intuitively see the distribution of electron cloud in three-dimensional space.

Jihad Asad, Pravanjan Mallick, Mohammad Esmael Samei +4 more

Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding of the subject.

Arno Böhm, Mark E. Loewe