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An electron can be prepared in any (proper wave function) state where its confined to an arbitrarily small volume. In such a state its momentum wave function is in general necessarily diffuse; this diffuseness is regulated via the uncertainty principle. When its position is then really measured, the originally prepared wave function collapses into a certain eigenfunction of the Hamiltonian of the system with a probability proportional to the square abs value of the complex coefficient of the proportion that eigenfunction contributed to the originally prepared state. Also such eigenfunctions can be very strongly localized (e.g. particle in a box). Moreover in quantum mechanics the electron does not "travel" with some speed between some points in space, it has no trajectory. The wave functions much more show some time evolution which neither in the non-relativistic (Schrödinger eq.) nor the relativistic case (Dirac eq.) would inhibit it to "appear" (get probability amplitude) suddenly at places which it could not reach if it would be a particle obeying classic equations of motions. I think this can be seen in analogy to the famous tunneling where the electron can appear at classical "forbidden" regions.