Quantum Circular Box Applet,

The Simulating Two-Dimensional Energy States with a Quantum Circular Box Applet—originally created by Paul Falstad—is an interactive physics simulator designed to visualize the quantum mechanics of a single particle trapped inside a circular, infinite potential well. Core Quantum Concepts Simulated

The applet models how a particle behaves when confined to a 2D circular boundary. Because the boundary is circular, the Schrödinger equation is solved using polar coordinates instead of rectangular coordinates.

Wavefunctions: The allowed energy states are expressed mathematically as a product of a Bessel function (for the radial distance ) and a complex exponential (for the angular direction

Quantum Numbers: The states are defined by two main quantum numbers: (principal/radial nodes) and (angular momentum).

Phase vs. Probability: The applet uses brightness to display the probability density (

) of finding a particle, while different color hues represent the complex phase of the wavefunction. Key Visual Components of the Applet

The interface is split into three main regions to give a comprehensive view of the quantum state: Screen Section Visual Element & Purpose Top

Potential Well Cross-Section: Shows a side view of the deep well. Allowed energy levels are marked as horizontal lines. Center

Probability Distribution Graph: A 2D bird’s-eye view of the box. You see the physical shapes, rings, and lobes formed by the particle’s wave functions. Bottom

Phasor Array Matrix: A grid of small dials (spinors) representing individual energy eigenstates. Interactive Features & Controls

The applet allows users to actively manipulate quantum states rather than just observing them staticly:

Selecting Eigenstates: Double-clicking a single phasor at the bottom isolates a specific, pure energy state (a stationary state).

Creating Superpositions: Clicking and dragging individual phasors alters their magnitude and phase angle. This mixes states together, allowing you to watch the combined wavefunction evolve and fluctuate dynamically over time.

Gaussian Wave Packets: Dragging your mouse across the center 2D position graph generates a localized Gaussian wave packet. You can watch it spread out, bounce off the circular walls, and self-interfere.

Symmetry Tracking: Hovering over any energy level or phasor highlights all other states sharing that exact same energy level, making it easy to identify degenerate states. Technical Evolution

The simulation was originally deployed as a Java Applet. Because modern web browsers no longer natively support Java plugins, the simulation has been entirely rebuilt into an accessible HTML5/JavaScript SwingJS version. It now runs smoothly directly in any modern desktop web browser without requiring external installations.

Are you looking to use this applet for a specific course assignment, or Quantum Mechanics: 2-Dimensional Circular Box Directions