In the case of spin system, let's consider Sx be along X direction Sy be along Y direction and Sz be along Z direction. We know there is a finite probability for spin up and spin down states in these directions. If we apply magnetic field along any one direction, say, X direction. Then probability for finding particle in spin up state and spin down state both will be half along X axis. Why is it so? Even if we are measuring in X direction there is a finite probability along Y and Z directions why?
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