Infinite Square Well Calculator
Calculate energy levels and wave functions for a particle in an infinite square well
About this calculator
The Infinite Square Well Calculator computes energy levels and wave functions for a quantum particle confined in a one-dimensional box with infinite potential walls. This fundamental quantum mechanics model demonstrates particle quantization, where energy exists only in discrete levels proportional to n². The calculator helps students and researchers understand quantum confinement effects, energy quantization principles, and wave function behavior in bounded systems, making it essential for studying quantum mechanics fundamentals.
How to use
Enter the particle mass, well width, and quantum number (n) into the calculator. The tool will compute the corresponding energy level using the formula E = n²h²/(8mL²) and generate the normalized wave function ψ(x). Results show both numerical values and graphical representations of the wave function probability density.
Frequently asked questions
What is the ground state energy?
The ground state (n=1) has the lowest possible energy, equal to h²/(8mL²), where h is Planck's constant, m is mass, and L is well width.
Why can't n equal zero?
Quantum mechanics requires n ≥ 1 because n=0 would give zero energy and wave function, meaning the particle doesn't exist in the well.
How does well width affect energy levels?
Energy levels are inversely proportional to the square of well width. Narrower wells have higher energy levels due to increased quantum confinement effects.