A model is presented for the quantum memory, the content of which is a pure quantum state. In this model, the fundamental operations of writing on, reading, and resetting the memory are performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. An example, based on the Fermi pseudo-potential in one dimension, is used to demonstrate that the requirements on the scattering process are consistent and can be satisfied. This model is compared with the commonly used model for the quantum memory; the most important difference is that the spatial dimensions and interference play a central role in the present model.