A Bound states of an electron trapped in a dipole field

[reterty]

The problem of bound states of an electron trapped in a dipole field is being studied by Alhaidari and company. (See, for example, https://arxiv.org/ftp/arxiv/papers/0707/0707.3510.pdf). It is not clear to me why the point dipole approximation is used everywhere in such calculations. Can't an electron in such a system be localized at distances of the order of a dipole size, where it is necessary to honestly, without Taylor, take an expression for the potential energy of a system of two oppositely charged immovable centers?

 

[DrClaude]

My guess is that using a point dipole is the only way to get an analytical solution. It is an interesting toy problem, but I don't think anybody uses such a model for actual molecules.