# The Heun differential equation and the Gauss differential equation related to quantum walks

@article{Konno2011TheHD, title={The Heun differential equation and the Gauss differential equation related to quantum walks}, author={N. Konno and T. Machida and Tohru Wakasa}, journal={arXiv: Quantum Physics}, year={2011} }

The limit theorems of discrete- and continuous-time quantum walks on the line have been intensively studied. We show a relation among limit distributions of quantum walks, Heun differential equations and Gauss differential equations. Indeed, we derive the second-order Fucksian differential equations which limit density functions of quantum walks satisfy. Moreover, using both differential equations, we discuss a relationship between discrete- and continuous-time quantum walks. Taking suitable… Expand

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