In this study, we address the challenge of solving the time-independent Schrodinger equation for the quantum harmonic ¨ oscillator, a key concept in quantum physics, by employing two prominent numerical methods: the Shooting method and the Numerov method. Our investigation focuses on deriving numerical solutions for the oscillator’s energy levels and wave functions, and then see how these solutions match up with the known analytical results. Through a detailed analysis including accuracy, computational efficiency, and the ability to accurately represent both ground and excited states, this paper aims to find the most suitable numerical approach for tackling quantum mechanical problems. By doing this, we provide insights into how these numerical methods can be used in quantum physics, making our findings useful for those looking to understand or research in this area.
Tools: Python
Department: Department of Mathematics
Project Poster
