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We usually see in 3d potential problems, that we consider potential to be separable as a sum of three independent one dimensional like potential, for all three variables, i.e

$$V(x, y, z)=V(x)+V(y)+V(z).$$

Does this happen for any real potential we deal with in real life?

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    $\begingroup$ The central potential leads to separable solutions in spherical coordinates. $\endgroup$
    – ZeroTheHero
    Commented Nov 19, 2022 at 3:00
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    $\begingroup$ This isn't what separable means - separable would be $V(x,y,z) = X(x)Y(y)Z(z)$. This is very common, and it is useful because it means $\frac{1}{V}\frac{d}{dx_i}V = \frac{1}{X_i(x_i)}\frac{dX_i(x_i)}{dx_i}$ $\endgroup$
    – Señor O
    Commented Nov 19, 2022 at 8:50

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