Application of the Peter Chew Complex-Coefficient Quadratic Equation Method in Quantum Mechanics: A Simplified Framework for Natural Energy Computation

Application of the Peter Chew Complex-Coefficient Quadratic Equation Method in Quantum Mechanics: A Simplified Framework for Natural Energy Computation | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 24 November 2025 V1 Latest version Share on Application of the Peter Chew Complex-Coefficient Quadratic Equation Method in Quantum Mechanics: A Simplified Framework for Natural Energy Computation Author : Prof. Dr. Peter Chew 0000-0002-5935-3041 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176402465.57701746/v1 144 views 84 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Building on the demonstrated success of the Peter Chew Complex-Coefficient Quadratic Equation Method (PCCQEM) in fields such as electromagnetic, this paper extends its application to quantum mechanics. In quantum physics, determining the energy eigenvalues of a system often requires solving characteristic equations with complex coefficients, which represent interaction potentials or dissipative effects. Traditional algebraic methods for solving these equations are notoriously cumbersome, often involving more than a dozen error-prone steps. This paper illustrates how PCCQEM streamlines the computation of complex energy states into a concise five-step mnemonic-based process (PETER). Through a comparative analysis of a representative quantum problem, we demonstrate that PCCQEM drastically reduces computational complexity and minimizes the potential for algebraic error. By simplifying the mathematical procedure, the method enables physicists to focus on the physical interpretation of energy states rather than tedious manipulation. The findings establish PCCQEM as a powerful and reliable tool for both educational and research applications in quantum mechanics, offering efficiency, accuracy, and pedagogical clarity in tackling complex eigenvalue problems. Supplementary Material File (24-11-25 quantom mechanic.pdf) Download 421.43 KB Information & Authors Information Version history V1 Version 1 24 November 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords complex energy states complex-coefficient quadratic equations energy eigenvalues pccqem peter chew method quantum mechanics schrödinger equation Authors Affiliations Prof. Dr. Peter Chew 0000-0002-5935-3041 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 144 views 84 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Prof. Dr. Peter Chew. Application of the Peter Chew Complex-Coefficient Quadratic Equation Method in Quantum Mechanics: A Simplified Framework for Natural Energy Computation. Authorea . 24 November 2025. 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