the first quantization, the Klein-Gordon (KG) equation in the vector potential separates into each Fourier mode for the time-dependent electric field [@KLY08], while the KG equation in the time-dependent magnetic field does not separate into each harmonic wave function, which corresponds to an instantaneous Landau state as shown in Ref. [@kim14a]. In fact, the KG equation in a time-dependent magnetic field in the two-component first-order formalism [@kim14a] is equivalent to the Wheeler-DeWitt equation for the Friedmann-Robertson-Walker universe minimally coupled to a massive scalar field [@kim92; @kim13]. Interestingly, the third quantized universe coupled to a massless scalar is equivalent to a system of infinite number of decoupled oscillators with a time-dependent mass and time-dependent frequencies [@kim14b], which is analogous to the charged field in a time-dependent electric field.

The functional Schrödinger picture provides a second quantized field theory, which extends the time-dependent Schrödinger equation for quantum mechanical systems to quantum fields [@FHM85; @guth-pi85]. Thus, in the second quantized scalar field, the quantum theory is the functional Schrödinger equation with time-dependent Hamiltonians for a charged scalar field in external electromagnetic fields. In the first case of time-dependent electric fields, the Gaussian wave functional can be directly found in terms of the covariance 