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Using the shape invariance idea, it is shown that the quantum states of Morse potential represent an infinite-dimensional Lie algebra the so-called Morse algebra. Then, we derive a representation of the Lie algebra u(1,1) by means of using the generators of the Morse algebra. Meanwhile, we obtain the BarutGirardello coherent states which are constructed as a linear combination of the quantum states corresponding to the Morse potential. Finally, we realise the resolution of the identity condition for the coherent states.
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