Starting with the well‐known de Broglie relation mv = h/λ that holds for a particle in zero magnetic field we give an elementary derivation of the generalized de Broglie relation that holds for a charged particle in a circular orbit in a cylindrically symmetric magnetic field. We make no use of ’’div, grad, curl, and all that’’ and do not introduce canonical momentum, the vector potential, or the Schrödinger equation. This generalized de Broglie relation is then assumed to hold for each of the Cooper pairs in a superconducting hollow cylinder. With the further assumption of the Meissner effect we find the well‐known result φ = nh/q for the flux φ trapped by the circulating Cooper pairs of charge q = 2e. We then use the generalized de Broglie relation to show that the Cooper pairs have velocities about 10−6 times too small for them to be in equilibrium ’’cyclotron orbits’’ in the magnetic field they experience. We also show that this de Broglie relation gives the correct value (i.e., the Schrödinger theory value) for the London penetration distance.
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Papers| June 01 1982
Elementary derivation of the magnetic flux quantum
Am. J. Phys. 50, 514–516 (1982)
Frank S. Crawford; Elementary derivation of the magnetic flux quantum. Am. J. Phys. 1 June 1982; 50 (6): 514–516. https://doi.org/10.1119/1.12799
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