I am studying the different probability interpretations (frequentist, bayesian etcetera) but for me it keeps bugging that since the probability density function in quantum mechanics is found by finding the modules of the wave function that satisfies schrödingers equation it seems to me that these wave functions are more fundamental than the concept probability itself.
In that sense probability emerges from a physical theory. What is the significance of the wave function being more fundamental than the probability in quantum mechanics?