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Which of the following is the correct mathematical representation of the Schrodinger wave equation fAtomic Structure Chemistry Question

Question

Which of the following is the correct mathematical representation of the Schrodinger wave equation for a hydrogen atom using the Laplacian operator ($\nabla^2$)?

Answer: B

💡 Solution & Explanation

The Cartesian Schrodinger equation is $\frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} + \frac{\partial^2\psi}{\partial z^2} + \frac{8\pi^2m}{h^2}(E-V)\psi = 0$. Substituting the Laplacian operator $\nabla^2$ gives $\nabla^2 \psi + \frac{8\pi^2m}{h^2}(E - V)\psi = 0$.

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