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The rolling sphere, the quantum spin, and a simple view of the Landau–Zener problem

Alberto G. Rojo, Anthony M. Bloch
2010 American Journal of Physics  
We consider the problem of a sphere rolling on a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin precession. As an interesting example we show that the Landau-Zener problem corresponds to the rolling of a sphere on a Cornu spiral, and derive the probability of a non-adiabatic transition using the rolling language. We also discuss the
more » ... discuss the adiabatic limit and the vanishing of geometric phases for rolling on curved surfaces.
doi:10.1119/1.3456565 fatcat:ifm2yz3lpnd7tnhdeqdi47lomi