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Fradkin Tensor
The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after Josef-Maria Jauch and Edward Lee Hill and David M. Fradkin, is a conservation law used in the treatment of the isotropic multidimensional harmonic oscillator in classical mechanics. For the treatment of the quantum harmonic oscillator in quantum mechanics, it is replaced by the tensor-valued Fradkin operator. The Fradkin tensor provides enough conserved quantities to make the oscillator's equations of motion maximally Superintegrable Hamiltonian system, superintegrable. This implies that to determine the trajectory of the system, no differential equations need to be solved, only algebraic ones. Similarly to the Laplace–Runge–Lenz vector in the Kepler problem, the Fradkin tensor arises from a hidden Symmetry (physics), symmetry of the harmonic oscillator. Definition Suppose the Hamiltonian function, Hamiltonian of a harmonic oscillator is given by : H = \frac + \frac m \omega^2 \vec x^2 with * momentum \vec p, * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josef-Maria Jauch
Josef Maria Jauch (September 20, 1914 in Lucerne – August 30, 1974 in Geneva) was a Swiss/American theoretical physicist, known for his work on quantum electrodynamics and on the foundations of quantum theory, and leader of the "Geneva School" of mathematical physics. Biography Early life Jauch was born on 20 September 1914 in Lucerne, Switzerland, the son of Josef Alois Jauch (a telegraph operator) and Emma Laura Rosa Jauch (née Conti). He had two older siblings: Adelheid Jauch and Emil Josef Karl Jauch. After his mother died in 1916, his father remarried, and a half-sister was born: Margrit Jauch (Fuchs). At the age of twelve he became fascinated with a fact he found stated in a popular astronomy book, that a body in a circular orbit with period T, if brought to a stop, would fall into the central mass in time T/\sqrt, which he showed could be derived from Kepler's laws of planetary motion, Kepler's law. Jauch was also interested in music, studying the violin from age twel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum (from Latin '' pellere'' "push, drive") is: \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
