The problem of wave propagation is very common in physics, and electromagnetic waves and acoustic waves are very common types of waves.  They have similar equation forms and reflection and refraction conditions, but they differ in terms of the number of polarization states and the total refraction conditions.  This paper mainly uses the eigenfunction method based on quantum mechanics to carry out theoretical calculations and numerical simulations, and obtains the refraction and reflection coefficients of electromagnetic waves and acoustic waves at the interface between two media. This method is more suitable for distinguishing the propagation direction of waves and can provide advantages in solving more complex wave equations.