The variational-relaxation algorithm for finding quantum bound states

2017/08/18 by Daniel V. Schroeder · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · doi:10.1119/1.4997165

openalex created_date 2017/02/10 · openalex publication_date 2017/08/18 · openalex updated_date 2026/07/28

Abstract

I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on the variational principle. It is especially useful for two-dimensional systems with nonseparable potentials, for which simpler techniques are inapplicable yet the computation time is minimal.

Cited by

• Proton-proton scattering on a quantum computer

Discussions

• In your finite difference method, instead of guessing E, you can use the calculated <E> for the trial psi and update this as you go along. See doi.org/10.1119/1.49... (free versions linked at physics. [bsky, 1 points, 3 comments]

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