According to the Accounting View of Money (AVM), the money issued by commercial banks in the form of demand deposits features a hybrid nature, since deposits can be shown to consist of a share of deposits bearing the characteristics of debt (debt-deposits) and a share of deposits bearing the characteristics of equity (equity-deposits), in a mix that depends on factors that relate to the issuing banks and the environment where they operate and interact, which may change over time. Following this important finding of the AVM, it is only consequential to associate the hybrid nature of bank deposits with the dual nature of the objects which is typical in quantum physics, and to investigate whether and how the application of quantum analytical methods and ideas to a form of money showing dualistic features could be used to extract valuable economic information. This article studies demand deposits (which represents the prevailing form of money in all contemporary economies) as a possible form of “money quanta”, that is, quantities reflecting some aspects tipical of quantum physics, and analyzes it using a quantum model to describe some relevant aspects of it, including for instance how banks’ power to create money (i.e., issue deposits typically via the credit channel) is affected by the interactions taking place between the banks and between the banks and their environments, and how system efficiency and stability change in relation to changes in bank behaviors. This article lays the foundations of money quanta and is the first step towards a better understanding of the relevance of quantum mechanical tools and ideas in connection with the study of economics and finance.