Few questions about double slit experiement How fast does the electron move in the experiment? If the electron moved nearly the speed of light and without any other forces, it must move in the straight line because Newton's first law of motion. If it not then what other forces effect on the electron?
If the electron shoot in the straight line, then how can it go through both slit? 
Does distance between an electron shooter and the slit matter in this experiment? What happen if the slit closer to the electron shooter?
Thanks, 
 A: If you increase the speed of the electrons then what changes is their momentum $p$. Then, through the de Broglie relation we know that the wavelength exhibited by those electrons is given by $\lambda = h/p$. In other words, the more momentum you give to the electrons, the shorter their wavelength, with the usual consequences for any diffraction properties.
Th rest of your question is a bit of a puzzle. Why do you worry about whether the electrons are travelling in straight lines, whereas you presumably accept that diffraction works for light, which is also supposed to travel in straight lines?
The distance between the source of collimated electrons and the slits does not matter.
The issue of which slit the electron goes through is the classic (if I can use that word!) wave-particle duality mystery. To get an interference pattern, the electron clearly goes through both slits. This is true even if you limit the electron flux so that there can only be one particle in the apparatus at a time. Any identification of which slit the electron goes through destroys the diffraction pattern. You will find much literature on this paradox.
A: I can understand your confusion on this topic. The standard way quantum mechanics is taught is that the Schrodinger equation is a tool for calculating the probabilities of outcomes of experiments, but that it is not literally true as a description of reality. Rather, somehow electrons really are little particles or something like that. But the Schrodinger equation is an accurate description of how the world works. What does it imply?
The electron is described by a state $|\psi(t)\rangle$, which might be described in terms of a sum of states $|R_j(t)\rangle$ for finding the electron in some region:
$$
|\psi(t)\rangle = \sum_j r_j|R_j(t)\rangle.
$$
If you measure which region the electron is in the resulting state is
$$
\sum_j r_j|R_j\rangle|M_j\rangle,
$$
where $|M_j\rangle$ is the state of the measuring apparatus for the electron being in $R_j$. The result of this is that there will be multiple versions of the measuring apparatus. These different versions don't interact with one another as a result of interactions with the outside world, see 
http://arxiv.org/abs/1212.3245.
The only thing that you can predict in advance about the measurement results is that you will see the jth result with probability $|r_j|^2$. This happens because there is no single fact of the matter about which result you will see before the measurement because there is no single fact of the matter about which region the electron is in.
Before the measurement there is no single fact of the matter about which region the electron is in. The subsequent amplitude for the electron to be in some particular place is dependent on what happens to each of the $|R_j(t)\rangle$ states, which will be something like
$$
|R_j(t_{later})\rangle = \sum_k \alpha(k) |R_k(t_{earlier})\rangle.
$$
The electron does not travel in a straight line. Nor does it do anything that resembles travelling in a straight line. Rather there are multiple instances of the electron, each of which is in some region, that interact in such a way as to give the appropriate amplitude for the electron to be in some region at a particular time. In general there is no single fact of the matter about which instance of an electron at one time corresponds to a given instance at some later time because the instances interact.
In the double slit experiment, different instances of the electron go through different slits. But those instances didn't travel in a straight line to get there because there is no such thing as one of those instances in isolation from the others. As a result you can sum over paths that are not straight lines to calculate the probability of finding an electron in a particular place as a result of an interference experiment:
http://arxiv.org/abs/1308.2022.
