Why an impact exerts so much force? If an object of velocity $v$ and mass $m$ moves towards a resting object of mass $M$, then if the object which is hit might break. Why? 
What is the reason that a collision has more power than a statical force $F$ acting on this object?
I haven't found any literature where such things are modeled. Can someone give literature where such things are described mathematically?
 A: To understand this, use the definition of force $\frac{d{\bf p}}{dt} = {\bf F}$, namely the force is equal to the rate of change of momentum. Something like a collision can be very complicated to model, but the average force is approximately given by ${\bf F}_{average} = \frac{\text{change in momentum}}{\text{time taken}}$. Typically, in a collision, the change of momentum is just the initial momentum, since afterwards the bodies are at rest. So, for any collisions, if you assume that the time taken for the collision is about the same (and can be of the order milli to tenths of a second), you get bigger (average) forces when the momentum change is bigger, namely when the initial momentum is larger. As an aside, not really useful to think of this as a problem in quantum mechanics.
A: Although the average force applied during a collision might be small enough that an object can take it, the peak force applied can be much higher. In physics this is called impulse.
Calculating the impulse for real world collisions (like a car crash) is very complicated. This is because cars have many structural members and the materials are not uniform. Depending on exactly how two objects collide, the forces can be applied to different members in different proportions and distributed around the object in different ways. This can cause forces to become concentrated on certain members, making them fail.
