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Sumudu Transform Homotopy Perturbation Method (STHPM), a hybrid algorithm that combines semi-analytical regime “Homotopy Perturbation Method” and an integral transform “Sumudu Transform” to evaluate precise solution of various types of Schrödinger equations, is introduced in the current research work. The mentioned equations in present research have a significant role in engineering and sciences, such as in propagation of optical pulses and waves in plasmas. A comparison of the approximated solution and the exact solution proves the legitimacy and effectiveness of this regime. Convergence analysis is also offered, and it confirms that the result of STHPM is convergent and distinct in character. Outcomes of STHPM are contrasted with precise answers. Additionally, 2D and 3D plots are covered. Current regime is a trustworthy method that may easily and accurately provide solution to a wide class of non-linear PDEs without need for discretization, complicated calculation, or linearization. It is error-free as well.