  In this paper, we will assume that the structure picture of the rotation
angles will be changed according to the scale of measurement (minimum
measurable angle) and if we have a device with very high accuracy (high
resolution) then we can notice a discrete nature of the rotations. We derived
the form of the angular momentum matrices and angular momentum operators in
this case and we find an indication of the need to change all quantum
mechanical operators at this very small scale (high energy level). As a
physical consequence, we calculated the magnetic quantum number and find that
it has been shifted to a fractional multiples of h and therefore the spin of
quantum particles is no longer take integer or half integer values but some
fractional values between them.
