Quantum Mechanics QM started out in the 1920s from a need to explain the mechanics/physics of the atom perceived to be composed of a $N$ negatively charged electrons attracted by a kernel with a positive charge balancing the electrons into a neutral atom. For the basic case of the Hydrogen atom with $N=1$ Schrödinger formulated in 1925 an eigenvalue problem for a wave function $\Psi (x)$ depending on a 3d space variable $x$ and $\Psi^2(x)$ representing electron charge density, expressing stationarity of a total energy composed of potential energy = $-\frac{\Psi (x)}{\vert x\vert}$ from kernel attraction and kinetic energy measured by $\frac{1}{2}\vert\nabla\Psi (x)\vert^2$ with $\nabla$ the gradient with respect to $x$, both integrated over $x$.
The ground state of minimal total energy as smallest eigenvalue is given by $\Psi (x)=\exp(-\vert x\vert)$ modulo normalisation, which expresses an electron charge density minimising kernel distance under gradient penalty. The observed spectrum of Hydrogen fits very precisely with differences of larger eigenvalues.
This was a formidable success, but the generalisation to atoms with $N>1$ showed to present difficulties which could not be overcome, and as a result QM turned away from the atom into abstractions of multidimensional wave functions representing not actualities of physical reality, but instead statistics of possibilities for more and more contrived experiments not with atoms but with photons of unknown physics.
The atom as the most stable predictable building block of the material world was thus turned into the unpredictable ball of a roulette table. This was a veritable collapse of scientific rationality into strange physics which has led into a permanent crisis of modern physics. Einstein and Schrödinger protested but where annihilated by Bohr using heavy artillery of strangeness and Born statistics. Check out RealQM as antidote.
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