# Quantum dynamics in potentials with fast spatial oscillations

## TL;DR

This paper investigates quantum systems with rapidly oscillating potentials, deriving an effective Schrödinger-like equation that reveals an attractive potential even when the average potential is zero.

## Contribution

It introduces a method using supersymmetric quantum mechanics to derive effective dynamics for systems with fast spatial oscillations, revealing new attractive potential effects.

## Key findings

- Effective Schrödinger-like equation derived
- Existence of attractive potential despite zero average
- Method applicable to rapidly oscillating quantum systems

## Abstract

We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective dynamics is governed by a Schr\"{o}dinger-like equation of motion and obtain the expression of the resulting effective Hamiltonian. In particular, we show that there exists an attractive effective potential even in the case when the oscillating potential averages to zero.