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Fradkin tensor
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<p>The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after <a href="/facts/Josef-Maria_Jauch/EP1dKJef">Josef-Maria Jauch</a> and Edward Lee Hill and David M. Fradkin, is a <a href="/facts/Conservation_law/6g1Ay2FR">conservation law</a> used in the treatment of the <a href="/facts/Isotropic/mc3QEY2x">isotropic</a> multidimensional <a href="/facts/Harmonic_oscillator/7IQNToGt">harmonic oscillator</a> in <a href="/facts/Classical_mechanics/ykG8upsN">classical mechanics</a>. For the treatment of the <a href="/facts/Quantum_harmonic_oscillator/JYA5J0h5">quantum harmonic oscillator</a> in <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, it is replaced by the tensor-valued Fradkin operator. </p><p>The Fradkin tensor provides enough conserved quantities to make the oscillator's <a href="/facts/Equations_of_motion/25msr1vE">equations of motion</a> maximally <a href="/facts/Superintegrable_Hamiltonian_system/XnpdUfJY">superintegrable</a>. This implies that to determine the <a href="/facts/Trajectory/STNN33FK">trajectory</a> of the system, no <a href="/facts/Differential_equations/9MGbE3Ca">differential equations</a> need to be solved, only algebraic ones. </p><p>Similarly to the <a href="/facts/Laplace%25E2%2580%2593Runge%25E2%2580%2593Lenz_vector/1gdBtfNj">Laplace–Runge–Lenz vector</a> in the <a href="/facts/Kepler_problem/oxyp49JD">Kepler problem</a>, the Fradkin tensor arises from a hidden <a href="/facts/Symmetry_(physics)/gJmgsooI">symmetry</a> of the harmonic oscillator. </p>