A memory is attributed to quantum systems. The time range of this memory is found to be inversely proportional to the energy of a system. The value of the wave function at any moment of time is the time average of its past values during the memory range. The formalism of quantum mechanics is reproduced in terms of integral operators and the time span of the memory of a system. The representation of the state of a quantum system at any moment of time is found to include an explicit representation of its past states as well. Measurement processes are explained from this point of view. Some experiments are analyzed using the present new interpretation.