London superconductivity approach in a time-dependent background

Highlights: • We introduce a new quantization scheme for the charge inside a superconductor. • We obtain the exact quantum solutions for charge space in a superconductor with time-dependent parameters. • We calculated the time-dependent uncertainties and the mean energy of the system. • Information measures, such as Shannon entropy and complexity were calculated. The main goal of this paper is to obtain the exact quantum solutions for charge space in a superconductor with time-dependent parameters using the London approach. We introduce a new quantization scheme for the charge inside a superconductor based on the Lewis and Riesenfeld invariant operator method. From the wave-functions obtained, we calculated the time-dependent uncertainties and the mean energy of the system. Information measures were also obtained, such as Shannon entropy and complexity. The later is always time-independent and also does not depend on conductivity. The other quantities are written in terms of a time-dependent function, $\rho \left(t\right)$, c-number quantity satisfying a nonlinear differential equation.