An isolated quantum system described by a wavefunction governed by an equation of motion, such as the Schrodinger equation: $$i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf{r},t)=\left[-{\frac {\hbar ^{2}}{2m}}\nabla^2+V(\mathbf{r},t)\right]\Psi (\mathbf{r},t)$$ If you might drop the time dependence in both the potential and the wavefunction you get a time independent equation. If you solve that equation for the Coulomb potential and the resulting wavefunction can be displayed to look like the clouds you see in many illustrations.

Now if you measure an electron during an interference experiment, then information about the electron spreads to other systems often called the environment, including whatever detector you use to measure the photon, and this produces an effect called decoherence that suppresses the interference:

https://arxiv.org/abs/quant-ph/0105127

https://arxiv.org/abs/1111.2189

Decoherence doesn't make quantum systems into particles it just suppresses interference on macroscopic scales for systems that interact heavily with the environment, like the objects you see around you.

How does this fit in with electron clouds? If an atom is interacting relatively weakly with its environment, then the evolution of the atom is dominated by its self Hamiltonian that describes the interaction between the proton and the electron. In these circumstances, decoherence tends to lead to the system being in an energy eigenstate, which doesn't change over time:

https://arxiv.org/abs/quant-ph/9811026

So treating the electron using the strategy outlined at the start of my answer can shed some light on features of real atoms. You can improve the approximation by using relativistic equations and introducing corrections for multiple electrons and so on.

An isolated quantum system described by a wavefunction governed by an equation of motion, such as the Schrodinger equation: $$i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf{r},t)=\left[-{\frac {\hbar ^{2}}{2m}}\nabla^2+V(\mathbf{r},t)\right]\Psi (\mathbf{r},t)$$ If you drop the time dependence in both the potential and the wavefunction you get a time independent equation. If you solve that equation for the Coulomb potential and the resulting wavefunction can be displayed to look like the clouds you see in many illustrations.

Now if you measure an electron during an interference experiment, then information about the electron spreads to other systems often called the environment, including whatever detector you use to measure the photon, and this produces an effect called decoherence that suppresses the interference:

https://arxiv.org/abs/quant-ph/0105127

https://arxiv.org/abs/1111.2189

Decoherence doesn't make quantum systems into particles it just suppresses interference on macroscopic scales for systems that interact heavily with the environment, like the objects you see around you.

How does this fit in with electron clouds? If an atom is interacting relatively weakly with its environment, then the evolution of the atom is dominated by its self Hamiltonian that describes the interaction between the proton and the electron. In these circumstances, decoherence tends to lead to the system being in an energy eigenstate, which doesn't change over time:

https://arxiv.org/abs/quant-ph/9811026

So treating the electron using the strategy outlined at the start of my answer can shed some light on features of real atoms. You can improve the approximation by using relativistic equations and introducing corrections for multiple electrons and so on.