Wave Function Analysis

Overview

This project is a computational study of quantum mechanical wave functions. It visualizes the probability distributions and time evolution of particles in various potential wells, providing insights into fundamental quantum behaviors.

Objectives

• Simulate the time-independent Schrödinger equation
• Visualize wave functions and probability densities
• Analyze particle behavior in infinite and finite potential wells
• Study tunneling effects and harmonic oscillators

Approach

Using numerical methods such as the Finite Difference Method, the Schrödinger equation was solved for different boundary conditions. Python libraries like NumPy and SciPy were utilized for computation, while Matplotlib created dynamic visualizations of the wave packet evolution.

Results

The simulation successfully modeled quantum systems, demonstrating discrete energy levels and tunneling phenomena. The visual outputs provided an intuitive understanding of abstract quantum concepts and validated theoretical predictions.