Because bitcoins processes depend on Internet transactions, one can argue that the dynamics of flux and volume of bitcoins might be subject to stochastic instead of a pure determinism event. By knowing that Quantum Mechanics describes well physics in the microscopic level and it is capable to calculate exact measurements of physical observables, we apply the concept of amplitude of probability to model the success probability of any transaction involving the new monetary unit so-called bitcoins. In this manner we focus on the description of the potential transactions using entirely the formalism of quantum mechanics. In addition we use also the concept of Green’s function that appear along the construction of the amplitude. Although not any direct correspondence can exist between the dynamics of flux of bitcoins and the purpose of a quantum theory, the modeling is limited to the extent of the interpretation of the success probability to complete any bitcoin-based transaction. For a transaction of N US dollars, we found that the bitcoin flux might reach up to a 90% of the completion of the transaction.