The time-independent Schrödinger wave equation for a single-electron system possessing total energy

Question

The time-independent Schrödinger wave equation for a single-electron system possessing total energy $E$ and potential energy $V$ is correctly formulated as

Professor PC Thomas Classes · Answer

(a) : The fundamental time-independent Schrödinger wave equation in three-dimensional space is rigorously represented as $
abla^2 \psi + \frac{8\pi^2 m}{h^2}(E - V)\psi = 0$, where the Laplacian operator is defined as $
abla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}$. This iconic differential equation mathematically models the dual wave-particle nature of an electron in an atom.