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We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model.We find that the boundary state of EOW brane is a coherent state of the$q$-deformed oscillators and the associated orthogonal polynomial is thecontinuous big $q$-Hermite polynomial. In a certain scaling limit, the big$q$-Hermite polynomial reduces to the Whittaker function, which reproduces thewavefunction of JT gravity with an EOW brane. We also compute the half-wormholeamplitude in DSSYK and show that the amplitude is decomposed into the trumpetand the factor coming from the EOW brane.

End of the world brane in double scaled SYK