A Gaussian function is a mathematical function characterized by its bell-shaped curve, defined by the equation $$f(x) = a e^{-rac{(x-b)^2}{2c^2}}$$, where 'a' is the peak height, 'b' is the position of the center of the peak, and 'c' controls the width of the bell curve. This function is crucial in quantum mechanics, particularly when dealing with wave functions and probability distributions, as it represents the spatial distribution of particles and their behaviors in various potential wells.
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