New derivation of Time-Independent Perturbation Theory

2023/03/27 by A. N. Kvinikhidze, Kvinikhidze, A. N., B. Blankleider +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Nuclear Theory (nucl-th) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2303.14862

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new derivation of Time-Independent Perturbation Theory (PT) that has a fundamental advantage over the usual derivations presented in textbooks on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can provide an easier and quicker way for students to learn PT, than afforded by current methods. In spite of that, our approach does not require the potentials to be energy independent or the inverse free Green function G₀^-1(E) to be a linear function of energy E, as is the case in QM, and can be applied directly to various extensions of QM including Relativistic QM, the Bethe-Salpeter equation, and all kinds of quasipotential approaches in Quantum Field Theory.

Related

• Time-dependent Perturbation Theory in Quantum Mechanics
• New Developments in Time-Independent Quantum-Mechanical Perturbation Theory
• Perturbation theory for bound states and resonances where potentials and propagators have arbitrary energy dependence
• Quantum mechanics in general quantum systems (II): Perturbation theory
• Exact solution and perturbation theory in a general quantum system