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Physics Final Year Topic: Grid-Convergence Study of Bound-State Energies in a One-Dimensional Finite Potential Well

This Physics final year project tests numerical eigenvalue estimates against boundary and grid-resolution choices.

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Why choose this project topic?

A focused study of finite-well eigenvalues gives you a specific question in quantum mechanics. It tests numerical eigenvalue estimates against boundary and grid-resolution choices. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do grid spacing and computational-domain size affect bound-state energy estimates for a stated finite potential well?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for finite-well eigenvalues with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for finite-well eigenvalues.
  2. 02Construct a documented discretised Hamiltonian and apply appropriate boundary conditions.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do grid spacing and computational-domain size affect bound-state energy estimates for a stated finite potential well?

A suggested research approach

Construct a documented discretised Hamiltonian and apply appropriate boundary conditions. Compare grid and domain refinements, check wavefunction normalisation and use an available analytical or high-accuracy reference for validation. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A stated finite-well Hamiltonian and units
  • Numerical eigenvalue software
  • Boundary, normalisation and convergence checks

Keep your project scope clear

A one-dimensional single-particle well is an idealised model and does not directly predict the full spectrum of a real atom or device.

Physics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

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