Numerical Methods for 1D Quantum Mechanics and Eigenvalue Analysis

Solving quantum mechanics problems analytically is often limited to a few classic scenarios, leaving numerical methods as the essential tool for real-world chemical physics and engineering applications. This course guides you from the foundational mathematical concepts of wave equations to implementing robust numerical solvers for one-dimensional quantum systems using matrix eigenvalue analysis. You will learn to translate continuous physical equations into discrete computer-readable models. What you'll learn: - Understand the foundational physics of the 1D Schrödinger equation and how to represent quantum states mathematically. - Apply finite difference methods to discretize continuous differential equations into matrix forms. - Construct Hamiltonian matrices using structured, vectorized code for efficient computation. - Solve matrix eigenvalue problems to find quantum energy levels and wavefunctions. - Analyze numerical stability, boundary conditions, and potential wells. - Practice writing clean, reproducible scientific scripts using modern matrix computation techniques. The course starts with key terminology, basic physical principles, and foundational definitions of wave mechanics before transitioning to discretization techniques. You will then progress step-by-step to building Hamiltonian matrices, executing eigenvalue solvers, and interpreting the physical meaning of your numerical outputs. This course is designed for beginners in scientific computing, chemical engineering, or physics who have basic linear algebra knowledge and want to learn numerical quantum modeling. Start mastering numerical quantum mechanics today through clear, step-by-step written explanations and practical coding exercises.