Back to Projects
Quantum Bound State Visualizer Banner

Quantum Bound State Spectrum Visualizer

An interactive simulation tool for exploring the discrete energy levels and wavefunctions of quantum particles in potential wells. By solving the Schrödinger equation numerically, this project highlights the effects of confinement, tunneling, and boundary conditions on wavefunction behavior.

Completed: November 2023 Quantum Mechanics & Numerical Simulation
Python NumPy Matplotlib SciPy
1D & 2D
Potential Support
±0.002 eV
Eigenvalue Accuracy
< 2 sec
Computation Time

Technical Overview

Core Concepts

The project numerically solves the time-independent Schrödinger equation...

Key Physics Aspects:

  • Finite difference approximations...
  • One-dimensional & two-dimensional potential well customizations
  • Visualization of wavefunction nodes...
  • Energy level spacing...

Simulation Architecture

The solver is implemented in Python using NumPy...

Software Layers:

  • Potential Interface:...
  • Eigenvalue Solver:...
  • Visualization Module:...
  • User Interaction:...
Wavefunction Distribution
Quantum Probaility Density

Technical Implementation

Numerical Solver

A finite-difference method approximates...


# Brief excerpt illustrating Hamiltonian construction & diagonalization
# ... (code remains same) ...
wavefunctions = eigenvectors[:, lowest_indices]

Potential Customization

Users can define various potentials...

Results and Analysis

Performance Metrics

  • Eigenvalue Accuracy:...
  • Computation Time:...
  • Potential Flexibility:...
  • Convergence:...

Educational Impact

The visualizer serves as a hands-on educational tool...

By adjusting parameters interactively...

Future Development

2D & 3D Extension

  • Expand solver...
  • Investigate multi-electron systems...
  • Visualize probability density...

GPU Acceleration

  • Leverage CUDA...
  • Enable higher discretization...
  • Reduce solve times...

Interactive UI

  • Implement a browser-based interface...
  • Real-time slider controls...
  • Automated result exports...
View on GitHub