# On an exactly solvable toy model and its dynamics

## TL;DR

This paper analytically solves the eigenstates and eigenenergies of a toy quantum model derived from a local quenched tight-binding system, providing insights into its dynamics and educational value.

## Contribution

It introduces an exactly solvable toy model for quantum dynamics, offering a new analytical approach and educational tool for quantum mechanics.

## Key findings

- Analytical solutions for eigenstates and eigenenergies
- Enhanced understanding of quantum dynamics in simplified models
- Educational value for undergraduate quantum mechanics

## Abstract

The eigenstates and eigenenergies of a toy model, which arose in idealizing a local quenched tight-binding model in a previous publication [Zhang and Yang, EPL 114, 60001 (2016)], are solved analytically. This enables us to study its dynamics in a different way. This model can serve as a good exercise in quantum mechanics at the undergraduate level.