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17. Mai 2024 · The failure of SO(3) to be simply connected is intimately connected to the distinction between integer spin and half-integer spin in quantum mechanics. Other examples of simply connected Lie groups include the special unitary group SU(n) , the spin group (double cover of rotation group) Spin(n) for n ≥ 3 {\displaystyle n\geq 3} , and the compact symplectic group Sp(n) .
Vor 5 Tagen · In quantum mechanics, the momentum and position wave functions are Fourier transform pairs, up to a factor of the Planck constant. With this constant properly taken into account, the inequality above becomes the statement of the Heisenberg uncertainty principle .
Vor 3 Tagen · Bessel function. Bessel functions describe the radial part of vibrations of a circular membrane. Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation.
Vor 4 Tagen · Quantum mechanics dictates, however, that angular momentum is quantized as a multiple of ħ, so therefore the product q e q m must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized.
Vor 2 Tagen · J. Robert Oppenheimer (born Julius Robert Oppenheimer; / ˈɒpənhaɪmər / OP-ən-hy-mər; April 22, 1904 – February 18, 1967) was an American theoretical physicist. He was director of the Manhattan Project 's Los Alamos Laboratory during World War II and is often called the "father of the atomic bomb ". Born in New York City, Oppenheimer ...
Vor 5 Tagen · Brilliant.org . Retrieved 16:32, May 23, 2024, from. At sufficiently small energies, the harmonic oscillator as governed by the laws of quantum mechanics, known simply as the quantum harmonic oscillator, differs significantly from its description according to the laws of classical physics. Whereas the energy of the classical harmonic oscillator ...
Vor 5 Tagen · Cluster of Excellence QuantumFrontiers – Light and Matter at the Quantum Frontier. In the Cluster of Excellence QuantumFrontiers, we use light and matter to extend the fundamentals and applications of metrology beyond the quantum limit. Participants in the cluster are Leibniz Universität Hannover, TU Braunschweig and the Physikalisch ...
