
QM Consilience_3_
... These probabilities are also invariant because they are defined solely in terms of the constants α and β. These four probabilities are postulated by the model. They are theoretically entities. Their measurement, or estimation, is determined from the available data in the same way that any theoretica ...
... These probabilities are also invariant because they are defined solely in terms of the constants α and β. These four probabilities are postulated by the model. They are theoretically entities. Their measurement, or estimation, is determined from the available data in the same way that any theoretica ...
Quantum Computing Lecture 1 What is Quantum Computing?
... In the second case (an EPR pair), measuring the first bit gives |0i or |1i with equal probability. After this, the second qubit is also determined. ...
... In the second case (an EPR pair), measuring the first bit gives |0i or |1i with equal probability. After this, the second qubit is also determined. ...
A Matrix Realignment Method for Recognizing Entanglement
... We develop a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the ...
... We develop a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the ...
Quantum Computing
... the magnetic resonance of molecules in a solution, and the list goes on. The basic problem that all these methods run into though is not how to create a Qbit, but how to get that Qbit to maintain its state for sufficiently long enough time to perform calculations. In order for a Qbit to properly hol ...
... the magnetic resonance of molecules in a solution, and the list goes on. The basic problem that all these methods run into though is not how to create a Qbit, but how to get that Qbit to maintain its state for sufficiently long enough time to perform calculations. In order for a Qbit to properly hol ...
Group Theory
... {Wy} of any similarity matrix may be regarded as symmetry adapted vectors, since the transformation formulas [29] represent the prototype of symmetrized states. The basic features of symmetrized states are that they are mutually orthonormal and they transform according to G unirreps. The computation ...
... {Wy} of any similarity matrix may be regarded as symmetry adapted vectors, since the transformation formulas [29] represent the prototype of symmetrized states. The basic features of symmetrized states are that they are mutually orthonormal and they transform according to G unirreps. The computation ...
Entanglement for Pedestrians
... {ei fj, i=1..m,j=1..n} is a basis for V1V2 Every vector in V1V2 is a sum of products; but not every vector is a product. If it is a product, then it is said to be non-entangled. ...
... {ei fj, i=1..m,j=1..n} is a basis for V1V2 Every vector in V1V2 is a sum of products; but not every vector is a product. If it is a product, then it is said to be non-entangled. ...
4 Operators
... If we have n independent wavefuctions each having the same eigenvalue a Ĥψi = aψi i = 1, 2, 3, · · · ...
... If we have n independent wavefuctions each having the same eigenvalue a Ĥψi = aψi i = 1, 2, 3, · · · ...
1 Complex Numbers in Quantum Mechanics
... as < x(t) >. ( We are abusing notation by using the same symbol for the classical position and the quantum operator. This is common practice in physics.) Since the expected value is real, certainly both positive and negative frequencies appear, just as in Eq.(3). Summary The really important points ...
... as < x(t) >. ( We are abusing notation by using the same symbol for the classical position and the quantum operator. This is common practice in physics.) Since the expected value is real, certainly both positive and negative frequencies appear, just as in Eq.(3). Summary The really important points ...
Max Born

Max Born (German: [bɔɐ̯n]; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics for his ""fundamental research in Quantum Mechanics, especially in the statistical interpretation of the wave function"".Born was born in 1882 in Breslau, then in Germany, now in Poland and known as Wrocław. He entered the University of Göttingen in 1904, where he found the three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of ""Stability of Elastica in a Plane and Space"", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.In the First World War after originally being placed as a radio operator, due to his specialist knowledge he was moved to research duties regarding sound ranging. In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees under Born at Göttingen, and his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.In January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. He emigrated to Britain, where he took a job at St John's College, Cambridge, and wrote a popular science book, The Restless Universe, as well as Atomic Physics, which soon became a standard text book. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, where, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Max Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe. He remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany. He died in hospital in Göttingen on 5 January 1970.