You often see in atomic and molecular physics texts that bonding occurs between two atomic orbitals when their wave functions are in phase. These pictures often depict the 'phase' as whether or not the wave function is positive of negative. This is obviously not the same as the complex phase component of the wave function. The $ p_z $ orbital is completely real: $$ \psi (r, \theta)\propto \frac{r}{a_o}e^{-r/2a_0}\cos\theta $$ While the $p_x$ orbital is actually complex: $$ \psi (r, \theta, \phi)\propto \frac{r}{a_o}e^{-r/2a_0}\sin \theta e^{i\phi} $$
But both these p orbitals have the same behaviour when bonding, as if their complex phases are the same. What is the difference between this atomic orbital 'phase' and the actual complex phase of the wave function?
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