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SpringerBriefs in physics

1925. “Atomic Theory and Mechanics”: From the Old Quantum Theory to Heisenberg’s Quantum Mechanics

Arkady Plotnitsky

Published Sep 4, 2012• 1 citation
Publisher
DOI
10.1007/978-1-4614-4517-3_3

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This chapter introduces Heisenberg’s trajectory from old quantum mechanics towards his quantum matrix mechanics. It shows his partnership with Born and for the study of the helium atom and molecules under the old quantum theory and his work on the core model to account for the anomalous Zeeman effect in collaboration with Landé. The collaboration between Heisenberg Kramers to present the treatment between matter and radiation under the scope of the old quantum mechanics is also displayed. Then, afterwards, it is shown the birth of the matrix mechanics by its three initial papers in 1925: the Heisenberg’s paper where he replaced the motion of the electron into its transition; the Born and Jordan’s paper where they placed Heisenberg equation into matrices and found the corresponding equation of motion and the commutator between linear momentum and position of the electron; the Heisenberg, Jordan and Born’s paper where they obtained the diagonal elements of the Hamiltonian matrix (the energy of a quantum state) and its application to one-electron harmonic oscillator. Dirac’s contribution to matrix mechanics is also introduced followed the application in the quantum angular momentum (184 words).
Of Werner Heisenberg's many contributions, two stand out. The first was matrix mechanics. It was the first form of what is called “the new quantum mechanics,” as compared to the “old quantum mechanics” of Bohr. Bohr's old quantum theory talked of electron orbits; these were themselves unmeasurable. Heisenberg found a way of putting what was measurable into a sort of table, called a matrix. He also recognized that measurement of the same properties, such as electron spin, could give different results. This led to his second great achievement, his uncertainty principle. Certain pairs of measurements, such as position and momentum, could not be simultaneously measured to any desired degree of accuracy. The more accurately measured the one, the less can be known about the other. This is not an experimental error. It is fundamental. Heisenberg is associated with another uncertainty: his role in attempting to build a German atomic bomb. What he actually did or did not do is still a matter of controversy.