Particle in a 1D Infinite Square Well

This is a simple Python simulation of a particle in a 1D infinite square well, also known as the particle in a box problem from quantum mechanics.

What’s This About?

In quantum mechanics, a particle confined to a box of width a can only occupy certain allowed energy levels. The particle's wavefunction (ψ) describes the probability of finding it at different positions inside the box.

Mathematically, the wavefunction and energy levels can be derived from the time-independent Schrödinger equation, which I’ve also solved in my handwritten notes for better understanding.

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About the Code

This Python code:

1. Calculates the wavefunction for a given energy level n.
2. Plots ψ(x) along the box.
3. Prints the allowed energy for that level.

Example:

• Width of the box: a = 1e-9 m
• Energy level: n = 3

The code uses NumPy for calculations and Matplotlib for plotting.

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How to Run

1. Make sure you have Python installed (3.8+).
2. Install dependencies:

pip install numpy matplotlib scipy