Quantum Mechanics Without Quantum

Recent posts have identified the roots of  textbook Standard Quantum Mechanics StdQM, as the essence of modern atomic physics, in the works by Planck in 1900 on blackbody radiation and by Einstein in 1905 on photoelectricity. 

Let us retrace how StdQM as based on Schrödinger's Equation SE from 1925 for the Hydrogen atom, connects back to the early work by Planck-Einstein who did not know of atoms.  

We recall that in an act of desperation Planck introduced the concept of smallest quantum (chunk) of energy $E=h\nu$ of a wave with frequency $\nu$ and $h$ a constant later named Planck's constant, in order to explain why the ultra-violet catastrophe of blackbody radiation does not take place, as the prime challenge to theoretical physics in 1900. Planck as leading physicist of the German Empire simply had to come up with an explanation. In a Faustian deal Planck gave up his soul deeply rooted in classical physics for statistics of quanta and saved the day to the German Empire, which he deeply regretted but could not reverse.

Einstein followed in 1905 by connecting the smallest quantum of energy $h\nu$ to an idea of light as consisting of particles later named photons carrying exactly the energy $h\nu$. Einstein used this idea to come up with an explanation of photoelectricity in his position as patent clerk in Bern, in desperate need of scientific publications to open the door to a university position.

So was a smallest chunk or quantum of energy $h\nu$ and a light particle/photon supposed to carry that quantum of energy, introduced into physics in desperate attempts to gain attention, but the scientific community remained skeptical. 

The SE of a Hydrogen atom of 1925 took the form of classical continuum wave mechanical model in terms of an electron charge density $\psi (x)$ depending on a 3d spatial coordinate $x$ in Coulomb interaction with a kernel, while carrying a certain energy measured by $\vert\nabla\phi (x)\vert^2$ named kinetic energy. The observed spectrum of Hydrogen as a certain set of discrete frequencies $\nu$ showed to fit very precisely with differences of eigenvalues of SE representing differences of energy levels of the electron representing beat frequencies of an electron oscillating between levels. This connected energy to frequency in the same way as Planck's energy quantum $E=h\nu$ and Einstein's photon of energy $h\nu$.

So was a connection created between (i) a concept of smallest quantum of energy $h\nu$ and (ii) the discrete spectrum of a classical continuous wave equation without presence of any smallest quantum of energy. 

So was stdQM born to form the essence of modern physics as radically new form of physics based on a radically new idea of a smallest quantum of energy, which was based on a mathematical model of classical form as SE where the smallest quantum of energy had no role to play.  

The result is a mismatch between classical continuum physics in the form of SE without quantum, and a proclaimed new form of physics with quantum. No wonder that StdQM is surrounded by confusion expressed as "nobody understands QM". 

RealQM is an alternative to StdQM in the form of classical continuum physics without quantum. Computational Blackbody Radiation explains blackbody radiation and photoelectricity without quantum.The mismatch is gone.