Computational projects with the Landau–Zener problem in the quantum mechanics classroom

• Published in: American journal of physics Vol. 91; no. 11; pp. 885 - 892
• Main Authors: Guttieres, Livia A. J., Petrović, Marko D., Freericks, James K.
• Format: Journal Article
• Language: English
• Published: Woodbury American Institute of Physics 01-11-2023; American Association of Physics Teachers (AAPT)
• Subjects: Algorithms; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computational mathematics; Computational methods; Equations of motion; Hamiltonian mechanics; Interaction picture; Landau-Zener problem; Numerical methods; Perturbation theory; Quantum computing; Quantum mechanics; Quantum physics; Quantum theory; Quantum tunneling
• ISSN: 0002-9505; 1943-2909
• DOI: 10.1119/5.0139717

The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. In addition, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.