The multi-dimensionality of the Schrödinger equation of stdQM defies direct interpretation of its wave functions as phenomena taking place in physical 3d space, and so to save the budding quantum mechanics from collapse an interpretation in terms of probability of electron particle configuration was invented by Max Born quickly after the formation of Schrödinger’s equation in 1926.
This was a Faustian deal, which has become the trade mark of modern physics, since it sold out the very soul of causality, determinism and rationality of classical macroscopic physics to gain the glory of a new world of microscopic physics in the hands of modern physicists.
Many prominent physicists including Schrödinger, Einstein and De Broglie protested to the deal of sacrificing the soul of physics, but Born in team with Bohr and Heisenberg took the game since the only possible interpretation of the multi-dimensional wave function was probabilistic. But the price was very big and has led to endless fruitless debate about mystics of atom physics without causality.
The multi-d Schrödinger equation presented itself as a formal (trivial) generalisation to atoms with many electrons of Schrödinger’s equation for Hydrogen with one atom and as a formality without derivation from physical principles. Physicists in charge of stdQM thus view Schrödinger’s equation as given by God and beyond human understanding, with the amazing capability of having solutions which always exactly with observations.
But is it really true that Schrödinger’s equation is given by God and that we know that it is perfect? No, Schrödinger’s equation is constructed by a purely formal (trivial) mathematical generalisation by human minds without physics input. Moreover, since solutions by multi-dimensionality cannot be computed, it is impossible to check if solutions always agree with observation.
The foundation of stdQM was thus shaky when it was laid in the late 1920s and it still is. This is the motivation for seeking a different generalisation to many electrons of Schrödinger’s equation for Hydrogen, and realQM then comes up as a natural candidate based on physical principles.