User:Patrick0Moran/Rewrite QM

N.B. This section is getting picked up by Google for some reason, but it is only a draft in progress.

rewrite of Introduction to quantum mechanics

temp notes

A Fourier series cam represent any 'arbitrary' periodic function as a sum of trigonometric functions with matching periods. Since trigonometric functions graph out as continua, the sums of trigonometric functions will also graph out as continua.

remainders

Almost everything now seemed to be accounted for, and if people were able to tolerate a photon that could be made to show itself in a wave guise but could also be made to show itself in a particle guise, then the universe might seem rational, knowable, and certain. But there remained one nagging question: "Why are some lines in the hydrogen spectrum (and in other spectrums) brighter than others? Their relative brightnesses are entirely stable, so there must be a reason for this phenomenon too." When that question was answered, a world of indeterminacy would be revealed. Einstein was entirely opposed to that world and declared, "God does not play dice with the universe!"

The new quantum mechanics

Yet another mystery: uncertainty

The next step in this process of discovery was the realization that the products of multiplying two of these matrices in two orders (as described briefly above) always produces a difference, and that difference accounts for the indeterminacy in Heisenberg's Uncertainty Principle. This difference turns out to be a small multiple of Planck's constant, h. Heisenberg could already see, on the night he made his breakthrough, that products of things like momentum and displacement were likely to be different if the order of computation were switched. At the time he saw a computational glitch that he might be able to work around somehow. Later it turned out that the computed differences corresponded to differences in the real world. The whole idea was so counter-intuitive that Heisenberg created an example, based on ideas common and acceptable to classical physics. Basically his argument was that even if one only accepted classical physics one would have to admit that trying to measure, e.g., the position of something at a certain time, meant that trying to find out how fast it had just traveled through that point could not be a true measure of the velocity because the act of measurement itself had radically altered the velocity. This thought experiment is called Heisenberg's microscope.

All moved to main article

checklist

1905 Einstein photoelectric effect explained by photons.
1913 Bohr explained Rydberg formula by hypoth that electrons revolve at quantum distances, each have an energy associated with so that electron movements between orbits require quantum emissions or absorptions of energy."The Rydberg formula, which was known empirically before Bohr's formula, is now in Bohr's theory seen as describing the energies of transitions or quantum jumps between one orbital energy level, and another."
1916 Sommerfekd suggested elliptical orbits to account for Zeeman effect.
1922 Stern and Gerlach discovered discrete values of angular momentum for atoms in the ground state passing through an inhomogeneous magnetic field leading to the discovery of the spin of the electron.
1923 Louis de Broglie Postulated that electrons in motion are associated with waves the lengths of which are given by Planck’s constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p.
1925 matrix mechanics, Heisenberg
1925 Pauli, exclusion principle
1926 Erwin Schrödinger Used De Broglie’s electron wave postulate (1924) to develop a “wave equation”

Discoveries

N -- Bohr L -- Bohr Ml -- Pauli Ms -- Goudsmit and Uhlenbeck

Bohr explained the Rydberg formula in terms of atomic structure. Q * relativity -- Dirac wave-particle duality de Broglie exclusion Pauli 1925

References