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    • https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/14%3A_Forces_in_Relativity/14.02%3A_Aharonov-Bohm_Effect
      If the potential energy of a particle is zero and both the kinetic and potential momenta point in the ±x direction, the total energy equation 14.7 for the particle becomes In particular, if the p...If the potential energy of a particle is zero and both the kinetic and potential momenta point in the ±x direction, the total energy equation 14.7 for the particle becomes In particular, if the potential momentum points in the same direction as the kinetic momentum, the total momentum is increased and the wavelength decreases, while a potential momentum pointing in the direction opposite the kinetic momentum results in an increase in wavelength.
    • https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/05%3A_Quantum_Electrodynamics/5.01%3A_Quantization_of_the_Lorentz_Force_Law
      We wish to formulate the Hamiltonian governing the quantum dynamics of such a particle, subject to two simplifying assumptions: (i) the particle has charge and mass but is otherwise “featureless” (i.e...We wish to formulate the Hamiltonian governing the quantum dynamics of such a particle, subject to two simplifying assumptions: (i) the particle has charge and mass but is otherwise “featureless” (i.e., we ignore the spin angular momentum and magnetic dipole moment that real electrons possess), and (ii) the electromagnetic field is treated as a classical field, meaning that the electric and magnetic fields are definite quantities rather than operators. (We will see how to go beyond these simpli…
    • https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/05%3A_Curvature/5.10%3A_From_Metric_to_Curvature
      The change in a vector upon parallel transporting it around a closed loop can be expressed in terms of either (1) the area integral of the curvature within the loop or (2) the line integral of the Chr...The change in a vector upon parallel transporting it around a closed loop can be expressed in terms of either (1) the area integral of the curvature within the loop or (2) the line integral of the Christoffel symbol (essentially the gravitational field) on the loop itself.

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