In this study, propagation of quantum waves through neurons has been studied via partial differential equations, a mathematical approach. Central to the exploration is a Schrödinger-like equation which models the quantum wave propagation in a neuron. The analysis delves into how the wave function, contingent on spatial position and time, is influenced by potential barriers and its initial conditions. Complimenting this is an equation capturing the dynamics of neurons. This equation underscores the relationship between the quantum wave function and the neuron firing rate. By employing a discretized spatial domain and initializing the wave function with a Gaussian wave packet, iterative numerical techniques have been utilized to glean insights into the temporal evolution of this function. The presented model is further refined by incorporating boundary conditions and additional equations that factor in external stimuli and neuronal connectivity. In conclusion, the presented mathematical framework hypothesizes connections between the probabilistic realm of quantum mechanics and the intricate existence of neuronal interactions. While awaiting empirical validation, the presented mathematical constructs pave the way for fresh perspectives and methodologies in understanding neural processes.