Abstract
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 the continuous big q-Hermite polynomial. In a certain scaling limit, the big q-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. We also compute the half-wormhole amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane.
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