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Abstract
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Two new configurations of superposition of quantum states corresponding to the angular momentum of spin-1 quantum system is proposed in this article. One is a trivial state,
, which consists of two Klauder’s type of spin coherent state and
that is also perpendicular to , and the other is a non-trivial case composed of vector
product of two different copies of spin states, and , i.e. .
Some properties of such quantum states are discussed. For instance, depending on the
particular choice of parameters, we show that they minimize both the Heisenberg and
Robertson-Schr dinger uncertainty relations (RSUR) of each pair of the angular momentum components while the standard spin-coherent states do not satisfy. We have also shown
that preparing the system state as a and choosing one of the mentioned orthogonal
states, , one can find a minimum lower bound for the Maccone-Pati uncertainty
relations (MPUR) which is stronger than the other uncertainties. We also establish an
irreducible and unitary representation of Lie algebra 2 through the introduced states
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