While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of episodic overdistribution and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e., a subadditive total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd et al. [1] for the episodic memory overdistribution in the experimental immediate item false memory paradigm [1–3]. Following the Hamiltonian method of Busemeyer and Bruza [4] our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters—γc for recollection capability of cues, κp for bias or description-dependence by probes and β for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β is real. Only for complex β a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.