Quantum circuits in the presence of a magnetic field

In the present work, we consider a quantum LC circuit under a constant magnetic field. In particular, we derive a new discretized form of the Schrödinger equation, which is equivalent to introducing a potential in the pseudo-flux representation. We discuss the physical assumptions leading to our results, and using a direct numerical approach we calculate the energy spectrum of the LC quantum circuit as a function of a constant external magnetic flux. The results are compared with the spectrum obtained using the LiChen potential [Y. Q. Li and B. Chen, Phys. Rev. B 53 (1996) 4027]. Our results indicate that the energy spectra from both models are numerically different, hence they may be clearly distinguished under appropriate experimental conditions.