Lecture Notes on Quantum Computing

1. Numerically Solving Schrödinger Equations (1) by Christian Bauckhage.

Most quantum mechanical systems cannot be solved analytically and thus require numerical solution strategies. In this note, we look at one such strategy and discretize the Schrödinger equation which governs the behavior of a one-dimensional quantum harmonic oscillator. This leads to an eigenvalue / eigenvector problem over finite matrices and vectors which we then solve using standard NumPy functions.

2. Numerically Solving Schrödinger Equations (2) by Christian Bauckhage.

We revisit the problem of numerically solving the Schrödinger equation for a one-dimensional quantum harmonic oscillator. We reconsider our previous finite difference scheme and discuss how higher order finite differences can lead to more accurate solutions. In particular, we will consider a five point stencil to approximate second order derivatives and implement the approach using SciPy functions for sparse matrices.