To produce an elementary exposition of quantum physics, you must diffract particles through a slit (and then two slits).
When R.P. Feynman & A.R. Hibbs approached the slit in "Quantum Mechanics & Path Integrals" (McGraw Hill, 1965), using their path integral formulation of quantum mechanics, the math for a square slit required some nasty-looking definite integrals. So, they assumed that the profile of their slit was a smooth Gaussian function, rather than a harsh step-function, to make the math easier. And then they built on that result.
It's okay to simplify – to make the slit Gaussian – so you can do the math. Always respect the limitations of that result – view it as a first-estimate or starting-point, and work out how different things are for real-world slits, which are non-Gaussian.