[R] Hierarchical Representation and Propagation of Wavefunctions within Gaussian Basis Functions

## I. Introduction

This paper aims to provide an in-depth explanation of representing and propagating wavefunctions in a hierarchical manner using Gaussian basis functions. Wavefunctions are mathematical descriptions of the quantum states of physical systems and are fundamental to quantum mechanics. However, representing complex wavefunctions for real-world quantum systems remains a key challenge. This paper proposes using multiple layers of Gaussian basis functions, with trainable amplitudes, to represent wavefunctions in a hierarchical fashion and enable wavefunction propagation between layers.

Understanding …

functions hierarchical introduction machinelearning paper propagation quantum quantum mechanics representation systems world