The time-dependent Schrödinger wave equation is the basic partial differential
equation of quantum field theory. The study of this equation and its
applications play an exceptionally important function in modern physics. From
a mathematical point of view, the time-dependent Schrödinger equation is a
commutable as mathematics itself. The newest analytical methods to solve
linear and nonlinear differential equation is the Homotopy Perturbation Method
(HPM) developed to the time-fraction Schrödinger wave equation, which is a
combination of homotopy transformation and perturbation. Furthermore,
Picard Method (PM) is applied to formulate an approximate iterative solution
of the time-fraction Schrödinger equation.