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
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For the full publication, please contact the author directly at: praiseolorunmaiye567@gmail.com
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Institutions
- Covenant Polytechnic, Aba, Abia State 1
- Covenant University, Canaan Land, Ota, Ogun State 4
- Crawford University of Apostolic Faith Mission Faith City, Igbesa, Ogun State 2
- Crescent University, Abeokuta, Ogun State 1
- Cross Rivers University of Technology, Calabar, Cross Rivers State 142
- Delta State Polytechnic, Ogwashi-Uku, Delta State 11
- Delta State Polytechnic, Otefe, Delta State 13
- Delta State University, Abraka, Delta State 139
- Ebonyi State University, Abakaliki, Ebonyi State 17
- Edo University, Iyamho, Edo State 10