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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- UMA UKPAI SCHOOL OF THEOLOGY, UYO, AKWA IBOM STATE (AFFL TO UNIVERSITY OF UYO) 1
- Umaru Ali Shinkafi Polytechnic, Sokoto, Sokoto State 24
- Umaru Musa Yaradua University, Katsina, Katsina State 28
- Umca, Ilorin (Affiliated To University of Ibadan), Kwara State 1
- University of Abuja, Abuja, Fct 116
- University of Africa, Toru-Orua, Bayelsa State 4
- University of Benin, Benin City, Edo State 362
- University of Calabar Teaching Hospital School of Health Information Mgt. 1
- University of Calabar, Calabar, Cross River State 240
- University of Ibadan, Ibadan, Oyo State 14