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
- Sokoto State University, Sokoto, Sokoto State 42
- St. Albert The Great Major Seminary, Abeokuta. (affl. To University of Benin) 1
- Sule Lamido University, Kafin Hausa, Jigawa State 4
- Tai Solarin University of Education, Ijagun, Ogun State 18
- Tansian University, Oba, Anambra State 1
- Taraba State University, Jalingo, Taraba State 32
- Temple-Gate Polytechnic, Osisioma, Abia State 1
- The Oke-Ogun Polytechnic, Saki, Oyo State 6
- The Polytechnic, Ibadan, Oyo State 13
- THOMAS ADEWUMI UNIVERSITY, OKO-IRESE, KWARA STATE 1