##### volume **II:** Synopsis

#### part III: Modern Physics

### page 18: Quantum mechanics

Quantum mechanics began with the work of Max Planck at the turn of the twentieth century. It took nearly thirty years to reach its modern form, largely because the ideas it introduced into physics were very new and strange. The development of quantum mechanics was driven by a growing list of inconsistencies observed between Newtonian physics and observations of the microscopic world of atoms, electrons, photons and other particles. Quantum mechanics - Wikipedia

The historical roots of quantum mechanics lie in the relationship between matter and radiation. Hot matter emits electromagnetic radiation. In 1859 Kirchoff used a thermodynamic argument to show that the rate of emission of radiation from a body was a function of the temperature of the body and the frequency of the radiation only. He wrote 'it is a highly important task to find this function'. Gustav Kirchoff - Wikipedia

Max Planck found that function in 1900, but to provide a plausible derivation of it, he had to make an 'act of desperation': he assumed that the exchange of energy between material oscillators and the electromagnetic field was constrained by the relationship *E = hf*, where *E* is the energy,* f* the frequency of the radiation, and *h* a universal constant (*Planck's constant*). Pais page 372. Planck's discovery came amidst a growing body of experimental data that seemed impossible to explain using Newtonian physics. Planck's Law - Wikipedia

Of particular interest were the spectra of atoms. Systematic measurement of atomic spectra had begun in the middle of the nineteenth century, and by the end of the century spectroscopists, as measurers of spectra are called, were making measurements of very high precision.

Each atom can radiate and absorb across a spectrum of 'spectral lines'. Each spectral line has a fixed measurable frequency that seems to be determined by nature to unlimited precision. Classical physics could not explain this. The first quantum explanation was due to Niels Bohr, who found that he could explain the Rydberg-Ritz combination principle by assuming that the electronic orbits in the hydrogen atom were separated by one quantum of angular momentum. Rydberg-Ritz combination principle - Wikipedia, History of quantum mechanics - Wikipedia, Niels Bohr - Wikipedia

Bohr's model worked well for hydrogen but would not work for more complex atoms. The final answer came in two forms. In 1925 Werner Heisenberg published his first paper on 'matrix mechanics'. In 1926 Erwin Schrödinger published the Schrödinger (energy) equation, laying the foundation of 'wave mechanics'. Both took account of the interactions between all the electronic orbits in an atom, an approach found necessary to model the energy of the atomic spectral lines correctly. Werner Heisenberg - Wikipedia, Schrödinger equation - Wikipedia

Both approaches to quantum mechanics were soon shown to be mathematically equivalent. This demonstration, took advantage of the mathematical theory of function spaces. This theory has been developed by David Hilbert, among others, and took advantage of Cantor's invention of set theory and of transfinite numbers. As in the case of Newton and calculus, it took a major advance in mathematics to produce a system powerful enough to model the complexity of the physical Universe. David Hilbert - Wikipedia

[revised 23 May 2013]