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
- Federal University of Technology, Minna, Niger State 47
- Federal University of Technology, Owerri, Imo State 95
- Federal University Oye-Ekiti, Ekiti State 41
- Federal University, Birnin-Kebbi, Kebbi State 37
- Federal University, Dutse, Jigawa State 6
- Federal University, Dutsin-Ma, Katsina State 63
- Federal University, Gashua, Yobe State 3
- Federal University, Gusau, Zamfara State 14
- Federal University, Kashere, Gombe State 1
- Federal University, Lafia, Nasarawa State 6