Authors : Aramide, T. M.; Olorunmaiye, P. F.; Abdulwareez, A.

Volume/Issue : Volume 10 - 2025, Issue 1 - January

Google Scholar : https://tinyurl.com/47h4fumw

Scribd : https://tinyurl.com/42jd7pfr

DOI : https://doi.org/10.5281/zenodo.14737860

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 (insert method, e.g., Lie algebraic techniques, supersymmetric quantum mechanics, or a novel approach). 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 : One Dimensional Anharmonic Oscillator, Quantum Mechanics, Nonlinear Potential, Schrodinger Equation, Energy Spectrum.

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