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We provide a formula for computing the overlap between two GeneralizedCoherent States of any rank one simple Lie algebra. Then, we apply our formulato spin coherent states (i.e. $\mathfrak{su}(2)$ algebra), pseudo-spin coherentstates (i.e. $\mathfrak{su}(1,1)$ algebra), and the$\mathfrak{sl}(2,\mathbb{R})$ subalgebras of Virasoro. In all these examples,we show the emergence of a semi-classical behaviour from the set of coherentstates and verify that it always happens when some parameter, depending on thealgebra and its representation, becomes large.

A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra