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evidence: In quantum mechanics , a doublet is a mixed quantum state of a system with a spin of 1 / 2 , such that there are two allowed values of the spin component , − 1 / 2 and +1  /  2 .. quantum mechanics. quantum mechanics. mixed quantum state. mixed quantum state. spin. spin ( physics ). Quantum systems with two possible states are sometimes called two-level systems .. Essentially all occurrences of doublets in nature arise from rotational symmetry ; spin 1 / 2 is associated with the fundamental representation of the Lie group SU -LRB- 2 -RRB- , the group that defines rotational symmetry in three-dimensional space .. spin. spin ( physics ). rotational symmetry. rotational symmetry. fundamental representation. fundamental representation. Lie group. Lie group. group. group theory