On the existence of solution to quantum impulsive dynamic equations on time scale

We extend the first-order impulsive dynamic equation on time scales to the frame work of quantum stochastic calculus, following the Hudson and Parthasarathy formulation within a specific locally convex space. Our primary contribution is proving the existence of solutions for the quantum impulsive dynamic equation on time scales with infinite delay. By defining an appropriate phase space and imposing necessary constraints, we employ the non-commutative versions of the LeraySchauder and Arzelầ fixed point theorems to demonstrate the existence of solutions.