Schrödinger's equation SE in its linear multi-dimensional form with wave function solution $\Psi (x)$ depending on a $3N$-dimensional spatial variable $x$ for a system with $N$ electrons is viewed to be the foundation of quantum mechanics of atoms and molecules as Standard Quantum Mechanics StdQM.
Without SE physics would be thrown back to 1924 with only Bohr's model of the atom in a form of classical physics. There are no physicists of today that advocate that this makes any sense.
But SE has been subject to deep dispute since its formulation by Schrödinger in 1926 followed by Born's suggestion of giving the wave function $\Psi (x)$ a meaning by saying that $\vert\Psi (x)\vert^2$ represents the probability of an electron configuration described by $x$. This means that $\Psi (x)$ is given an epistemic meaning as what "a physicist can say", and not an ontic meaning as physics independent of what a physicist may have to say, as expressed by Bohr.
But Bohr's view was not satisfactory to many physicists who wanted to find an ontic meaning of $\Psi$ independent of what people may have to say, but nothing really convincing was ever found. The $3N$-dimensionality of $\Psi (x)$ defied real physical meaning and then the only option was an epistemic statistical meaning.
This means that the basic foundational problem of SE has never been resolved despite intense debate over 100 years with no consensus in reach, except an agreement that after all the physical meaning of $\Psi (x)$ does not matter much, since it has shown to always deliver predictions in full agreement with observations, but then predictions with unclear physical meaning of course.
But there is an alternative to StdQM which could have been formulated in 1926, but for some reason was missed, see this post. This is RealQM as a different form of Schrödinger's equation as a non-linear system of one-electron wave functions $\psi_i(x)$ for $i=1,...N,$ with non-overlapping supports depending on a common 3d space variable $x$ with $\vert\psi_i(x)\vert^2$ as physical charge density with direct ontic meaning.
Connecting to the previous post, RealQM can be seen as a Platonic/mathematical generalisation from $N=1$ to $N>1$ where the physicality for the Hydrogen atom with $N=1$ is kept. On the other hand, StdQM can be seen as an Aristotelian/pseudo-mathematical generalisation where physicality is lost.
When I present RealQM as an alternative to StdQM to quantum physicists and chemists I meet little understanding indicating that the pseudo-mathematization of StdQM has a very strong grip of minds. Nor do mathematicians show interest because StdQM already in 1933 by the mathematician von Neumann was translated into an impressive abstract world of Hilbert spaces occupied by multi-dimensional wave functions subject to Hermitian operators satisfying axioms without physics.
But there is a good chance the situation can change in 2026 since RealQM is continuing to deliver new results in accordance with observations.
PS Bohr claimed that the purpose of quantum mechanics is to make predictions of experiments as testable events, not to compute e g the energies of ground state or excited state of an atom regardless of actual experiment being made. This opened to a confusion between deterministic computation of ground/excited state and probabilistic outcome of an experiment suggesting that the model behind the computation itself is of probabilistic nature although in fact fully deterministic. There is nothing probabilistic with the spectrum of an atom as difference between energies of ground/excited states, nor in computation nor in experiment except those from external inputs.
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