To get a wave function one has to solve the quantum mechanical equation for the boundary conditions of the experiment:"electron impinging on two slits". In the usual description one is using approximations : the incoming electron is a plane wave, the effective potential of the electrons in the matter of the slits is high. Then the distance between slits and the width of the slits is chosen commensurate to the de Broglie wavelength of the incoming electron, so that the dx*dp> h_bar/2 limit is binding and the quantum mechanical nature of the problem is apparent.

Question: how does the wave function that describes the atoms around the slit 'know' to interact with the wave function of the electron?

An effective potential approximates the collective behavior of the atoms around the slit.

Does it collapse?

Collapse is a bad terminology for interaction. The electron scatters off the collective potential of the atoms' electric field.

The reason I ask this is because when the electron does not make it through the slit, it must have collided with one of the atoms: but wouldn't collision imply that two particles were at the same place at the same time?

Do nor forget this is quantum mechanics. There exists a probability for the electron to scatter off or be absorbed by the atoms composing the slit. When the dimensions are chosen correctly, i.e. electron momentum, slit distances and width of slits, then the probability of going through is high and the interference pattern will be seen.

Doesn't that require wave function collapse?

Every measurements contributes to build the probability distribution for the problem at hand, i.e. the interference pattern is the complex conjugate square of the wavefunction for this set up . Each electron contributes a point on this distribution, showing how it interacted with the topology of the problem. The wavefunction is a general wavefunction for the setup and each electron gives one point by interacting with the recording screen. That is when the wave function "collapses" (I dislike the term, the wave function is not a balloon).

To get a wave function one has to solve the quantum mechanical equation for the boundary conditions of the experiment:"electron impinging on two slits". In the usual description one is using approximations : the incoming electron is a plane wave, the effective potential of the electrons in the matter of the slits is high. Then the distance between slits and the width of the slits is chosen commensurate to the de Broglie wavelength of the incoming electron, so that the $\Delta x \Delta p \geq \hbar/2$ limit is binding and the quantum mechanical nature of the problem is apparent.

Question: how does the wave function that describes the atoms around the slit 'know' to interact with the wave function of the electron?

An effective potential approximates the collective behavior of the atoms around the slit.

Does it collapse?

Collapse is a bad terminology for interaction. The electron scatters off the collective potential of the atoms' electric field.

The reason I ask this is because when the electron does not make it through the slit, it must have collided with one of the atoms: but wouldn't collision imply that two particles were at the same place at the same time?

Do nor forget this is quantum mechanics. There exists a probability for the electron to scatter off or be absorbed by the atoms composing the slit. When the dimensions are chosen correctly, i.e. electron momentum, slit distances and width of slits, then the probability of going through is high and the interference pattern will be seen.

Doesn't that require wave function collapse?

Every measurements contributes to build the probability distribution for the problem at hand, i.e. the interference pattern is the complex conjugate square of the wavefunction for this set up . Each electron contributes a point on this distribution, showing how it interacted with the topology of the problem. The wavefunction is a general wavefunction for the setup and each electron gives one point by interacting with the recording screen. That is when the wave function "collapses" (I dislike the term, the wave function is not a balloon).