Parallel Universes
... Sidebar: The Mystery of Probability: What really a separate universe, because it interacts with ours. But the Are the Odds? ensemble of universes--past, present and future--that these branes create would form a multiverse, arguably with a diversity similar to that produced by chaotic inflation. An i ...
... Sidebar: The Mystery of Probability: What really a separate universe, because it interacts with ours. But the Are the Odds? ensemble of universes--past, present and future--that these branes create would form a multiverse, arguably with a diversity similar to that produced by chaotic inflation. An i ...
On the speed of fluctuations around
... conditions are essentially the same as those in [9] but allow greater flexibility. Indeed, they New Journal of Physics 12 (2010) 055021 (http://www.njp.org/) ...
... conditions are essentially the same as those in [9] but allow greater flexibility. Indeed, they New Journal of Physics 12 (2010) 055021 (http://www.njp.org/) ...
Document
... in a Hilbert space can always be written as a pure state in a higher dimension Hilbert space Such that e.g., for the mixed state ...
... in a Hilbert space can always be written as a pure state in a higher dimension Hilbert space Such that e.g., for the mixed state ...
Universally valid reformulation of the Heisenberg uncertainty
... disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck’s constant when the intervention is dependent. A model of measuring interaction ...
... disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck’s constant when the intervention is dependent. A model of measuring interaction ...
PHYSICAL MEANING OF IMAGINARY UNIT i
... QM, made it absolutely impossible to imagine and conceive the real structure of individual atoms, which are three-dimensional structures. The removing of the third coordinate from the trio of the spherical polar coordinates (r , , ) is unjustified step invalid for any reason [4]. Ignorance of th ...
... QM, made it absolutely impossible to imagine and conceive the real structure of individual atoms, which are three-dimensional structures. The removing of the third coordinate from the trio of the spherical polar coordinates (r , , ) is unjustified step invalid for any reason [4]. Ignorance of th ...
Coherent States
... Here I digress from work in progress—namely, a review of a paper by C. Y. She & H. Heffner1 , which was the first of several papers inspired by E. Arthurs & J. L. Kelly’s “On the simultaneous measurement of a pair of conjugate observables” (BSTJ 44, 725 (1965)); it is my intention to incorporate tha ...
... Here I digress from work in progress—namely, a review of a paper by C. Y. She & H. Heffner1 , which was the first of several papers inspired by E. Arthurs & J. L. Kelly’s “On the simultaneous measurement of a pair of conjugate observables” (BSTJ 44, 725 (1965)); it is my intention to incorporate tha ...
Mathematical Aspects of Quantum Theory and Quantization Summer
... Physics as we know it, a successful combination of mathematical and experimental science , began in sixteenth and seventeenth century Europe, even though ancient and medieval civilizations, those of China, India, Greece and the Arab world for instance, were already in the possession of a considerabl ...
... Physics as we know it, a successful combination of mathematical and experimental science , began in sixteenth and seventeenth century Europe, even though ancient and medieval civilizations, those of China, India, Greece and the Arab world for instance, were already in the possession of a considerabl ...
10 Time Reversal Symmetry in Quantum Mechanics
... If x → x, p → −p under time reversal, then this commutation relation no longer holds. How to solve this problem? It was realized by Wigner that in quantum mechanics, time reversal has to be defined in a very special way different from all other symmetries. Time reversal operator is anti-unitary: it ...
... If x → x, p → −p under time reversal, then this commutation relation no longer holds. How to solve this problem? It was realized by Wigner that in quantum mechanics, time reversal has to be defined in a very special way different from all other symmetries. Time reversal operator is anti-unitary: it ...
Quantum Phase Transition and Emergent Symmetry in a Quadruple Quantum... Dong E. Liu, Shailesh Chandrasekharan, and Harold U. Baranger
... the Kosterlitz-Thouless (KT) type to a charge-ordered state (CO) (as in Refs. [8,9]) consisting of an unscreened doubly degenerate ground state [12]. Model.—The quantum dots in Fig. 1(a) are capacitively coupled in two ways: U is the vertical interaction (between Lþ and L ; Rþ and R ) and U0 is ...
... the Kosterlitz-Thouless (KT) type to a charge-ordered state (CO) (as in Refs. [8,9]) consisting of an unscreened doubly degenerate ground state [12]. Model.—The quantum dots in Fig. 1(a) are capacitively coupled in two ways: U is the vertical interaction (between Lþ and L ; Rþ and R ) and U0 is ...
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.