Following his doctoral studies he joined Janssen Pharmaceutica. He served as dean of his faculty between and Since he is a member of the Board of Directors of Ghent University. Later, he was member of the CDF collaboration that discovered in the top quark, one of the 12 elementary particles that constitute matter.
History of the formalism[ edit ] The "old quantum theory" and the need for new mathematics[ edit ] Main article: Old quantum theory In the s, Planck was able to derive the blackbody spectrum which was later used to avoid the classical ultraviolet catastrophe by making the unorthodox assumption that, in the interaction of electromagnetic radiation with matterenergy could only be exchanged in discrete units which he called quanta.
Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant, h, is now called Planck's constant in his honor.
Quantum projection noise thesisEinstein explained certain features of the photoelectric effect by assuming that Planck's energy quanta were actual particles, which were later dubbed photons. All of these developments were phenomenological and challenged the theoretical physics of the time.
Bohr and Sommerfeld went on to modify classical mechanics in an attempt to deduce the Bohr model from first principles. They proposed that, of all closed classical orbits traced by a mechanical system in its phase spaceonly the ones that enclosed an area which was a multiple of Planck's constant were actually allowed.
The most sophisticated version of this formalism was the so-called Sommerfeld—Wilson—Ishiwara quantization. Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom classically an unsolvable 3-body problem could not be predicted.
The mathematical status of quantum theory remained uncertain for some time. In de Broglie proposed that wave—particle duality applied not only to photons but to electrons and every other physical system.
The physical interpretation of the theory was also clarified in these years after Werner Heisenberg discovered the uncertainty relations and Niels Bohr introduced the idea of complementarity. The "new quantum theory"[ edit ] Werner Heisenberg 's matrix mechanics was the first successful attempt at replicating the observed quantization of atomic spectra.
Within a year, it was shown that the two theories were equivalent. It was Max Born who introduced the interpretation of the absolute square of the wave function as the probability distribution of the position of a pointlike object.
Born's idea was soon taken over by Niels Bohr in Copenhagen who then became the "father" of the Copenhagen interpretation of quantum mechanics. The correspondence to classical mechanics was even more explicit, although somewhat more formal, in Heisenberg's matrix mechanics.
In his PhD thesis project, Paul Dirac  discovered that the equation for the operators in the Heisenberg representationas it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson bracketsa procedure now known as canonical quantization.
Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his "index-schemes" were matrices, as Born soon pointed out to him.
In fact, in these early years, linear algebra was not generally popular with physicists in its present form. He is the third, and possibly most important, pillar of that field he soon was the only one to have discovered a relativistic generalization of the theory.
His work was particularly fruitful in all kinds of generalizations of the field. The first complete mathematical formulation of this approach, known as the Dirac—von Neumann axiomsis generally credited to John von Neumann 's book Mathematical Foundations of Quantum Mechanicsalthough Hermann Weyl had already referred to Hilbert spaces which he called unitary spaces in his classic paper and book.
It was developed in parallel with a new approach to the mathematical spectral theory based on linear operators rather than the quadratic forms that were David Hilbert 's approach a generation earlier.
Though theories of quantum mechanics continue to evolve to this day, there is a basic framework for the mathematical formulation of quantum mechanics which underlies most approaches and can be traced back to the mathematical work of John von Neumann.
In other words, discussions about interpretation of the theoryand extensions to it, are now mostly conducted on the basis of shared assumptions about the mathematical foundations.
Later developments[ edit ] The application of the new quantum theory to electromagnetism resulted in quantum field theorywhich was developed starting around Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the ones presented here are simple special cases.Cavity-Enabled Spin Squeezing for a Quantum-Enhanced Atomic Clock Abstract For the past decade, the stability of microwave atomic clocks has stood at the standard quantum limit, set by the projection noise inherent in measurements on ensembles of un- analytic quantum optomechanical model.
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Towards the Quantum Noise Limit in Ramsey-Bordé Atom Interferometry Von der Fakultät für Mathematik und Physik der Gottfried Wilhelm Leibniz Universität Hannover zur Erlangung des Grades The scheme allows now the quantum projection noise limited detection of 4· atoms.
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Item Type: Thesis (Dissertation (Ph.D.)).