Obtain three dimensional time independent Schrödinger’s wave equation.
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E = E1 + E2 + E3. One can now substitute these expressions into the full 3D Schrodinger equation and see that they solve it even at the points r where ψ(r) = 0. Therefore, the solution of the 3D Schrodinger equation is obtained by multiplying the solutions of the three 1D Schrodinger equations.
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