The Exact Solution of the One-Dimensional an Harmonic Oscillator

Student: Praise Folashade Olorunmaiye (Project, 2025)
Department of Physics With Electronics
Oduduwa University, Ipetumodu, Osun State

Abstract

The one-dimensional anharmonic oscillator is a fundamental problem in quantum mechanics, describing a particle subject to a nonlinear potential. While approximate solutions exist, exact solutions have remained elusive due to the complexity of the Schrodinger equation. This work presents an exact solution to the one-dimensional anharmonic oscillator using (Hermite series method. We derive the energy spectrum and wave function, revealing novel features and insights into the oscillator's behavior. Our exact solution enables precise calculations of physical quantities, such as expectation values and transition probabilities, without relying on approximations. This breakthrough has far-reaching implications for understanding nonlinear systems, quantum field theory, and condensed matter physics. The exact solution provides a benchmark for testing approximate methods and sheds new light on the intricate dynamics of anharmonic systems

Keywords
Anharmonic oscillator quantum mechanics energy eigenvalues wave function potential well exact solution Schrödinger equation non-linear systems quantum states perturbation theory
Filters
Institutions