Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase

We show the emergence of Berry phase in a forced harmonic oscillator system placed quantum space-time Moyal type, where time ‘t’ is also an operator. An effective commutative description gives dependent generalised with perturbation linear position and momentum. The then diagonalised to get its adiabatic evolution over time-period T studied Heisenberg picture compute expression geometric phase-shift.