One of the most "magical" aspects of quantum mechanics is tunneling—the ability of a particle to pass through an energy barrier that would be impassable in classical physics. Using MATLAB, students can simulate a wave packet incident on a potential barrier.
The use of MATLAB in an introductory course does more than just simplify math; it builds a bridge to professional science and engineering. Quantum computing, nanotechnology, and semiconductor design all rely on the computational modeling of quantum systems. Introductory Quantum Mechanics with MATLAB: For...
At the heart of quantum mechanics is the Schrödinger equation. While "pen-and-paper" solutions exist for simple systems like the harmonic oscillator or the hydrogen atom, most real-world quantum systems are analytically unsolvable. One of the most "magical" aspects of quantum
MATLAB excels at numerical integration and matrix manipulation. By discretizing space and representing the Hamiltonian operator as a matrix, students can use MATLAB’s built-in eigensolvers to find energy levels and stationary states. This "matrix mechanics" approach not only aligns with the fundamental principles laid out by Heisenberg but also prepares students for modern research in quantum chemistry and condensed matter physics. Simulating Quantum Tunneling and Scattering Simulating Quantum Tunneling and Scattering