Bohr, Heisenberg, Schrödinger, and the Principles of Quantum Mechanics

A Gaies, A. El Akrmi

A formal resemblance between thermodynamics and mechanics has been found. In this respect, the fundamental ideas of quantum theory can be obtained from this analogy. We have deduced a correspondence between Caratheodory's theorem and Bohr's stationary states principle. Using the deduced correspondence rules, we obtain the quantification rule of Bohr–Sommerfield. Also, starting from the theory of thermodynamic fluctuations, the Heisenberg uncertainty principle has been deduced without use of any quantum assumption. Our results show then that the Bohr–Sommerfield rule and Heisenberg's principle are the mechanical versions of thermodynamics laws. Exactly as the Schrodinger equation and the quantum mechanics pulse are the mechanical versions of the geometrical optics laws.

Abner Shimony

Michael Nauenberg

According to Heisenberg and Pauli, two of the great pioneers of quantum mechanics, in the domain of atoms and molecules the Bohr-Sommerfeld elliptic orbits disappear. But Bohr's correspondence principle requires that for large quantum numbers, quantum mechanics corresponds to classical mechanics. It is shown here how this correspondence, generally ignored in physics textbooks, takes place.

Abner Shimony

Sandro Petruccioli

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.