Quantum mechanics got a kick start in 1926 with Schrödinger’s wave equation for the Hydrogen one electron, with the wave function as a mimimiser over of the total energy
where , under the normalisation
The condition of minimality with respect to variations of takes the form of an eigenvalue problem
for the Hamiltonian
with a minimal eigenvalue and
The ground state can be computed analytically and is given by
The total energy to be mimimised is the sum of potential kernel energy
and what is normally referred to as kinetic energy, bur rather has the form of elastic compression energy:
The model thus involves two types of energy of a distributed charge density; potential energy and elastic energy and as such has the form of a classical model of continuum mechanics.
The whole conundrum of quantum mechanics is how to generalise the model to more than one electron. stdQM gives one answer and realQM another.