  In this paper, we explore the possibility of deriving a quantum wavefunction
for continuous-time recurrent neural network (CTRNN). We did this by first
starting with a two-dimensional dynamical system that describes the classical
dynamics of a continuous-time recurrent neural network, and then deriving a
Hamiltonian. After this, we quantized this Hamiltonian on a Hilbert space
$\mathbb{H} = L^2(\mathbb{R})$ using Weyl quantization. We then solved the
Schrodinger equation which gave us the wavefunction in terms of Kummer's
confluent hypergeometric function corresponding to the neural network
structure. Upon applying spatial boundary conditions at infinity, we were able
to derive conditions/restrictions on the weights and hyperparameters of the
neural network, which could potentially give insights on the the nature of
finding optimal weights of said neural networks.
