The general Schrödinger equation in 3d is $$i\hbar\frac{\partial\psi}{\partial t}(\mathbf r, t)=-\frac{\hbar^2}{2m}\nabla^2\psi(\mathbf r, t)+V(\mathbf r)\psi(\mathbf r, t).$$ Now consider that $$V(x, y, z)=\mathcal V(x)$$ for some univariate function $\mathcal V$. Then can we show that in this 1...