If we attempt to describe the solar system, we say that it has nine planets orbiting the sun in elliptical orbits. We can also find out the equations of the trajectories of the planets by choosing a co-ordinate system and tell the velocities at which they are moving at a given time to a very degree of precision. This way we can predict eclipses, transitions etc.
We can describe the motion of various machine parts similarly with accuracy.
We may similarly attempt to describe the motion of sub-atomic particles in terms of their paths, velocities etc.
BUT HERE WE FAIL.
We cannot study such systems with the help of familiar
Newton's laws of motion used to deal with macroscopic systems. The experimental results no longer match the theoretical results derived using the familiar laws of classical physics at this scale. So, do the laws governing the sub-atomic world different from the laws of the macroscopic world? The answer is NO.
The laws are the same - The laws of quantum physics. But the reason why we didn't require the laws before ( and why we couldn't discover them ) is that on a macroscopic scale, as an approximation, classical physics works pretty well and produces results that are in accordance with the experiments. But in a microscopic domain, their applications are limited.
At this scale we need to use laws like Heisenberg's Uncertainty Principle, Energy Quantization, Wave-Particle Duality etc. which are not important if we are dealing with larger particles but are nevertheless true for them too.
These laws are the foundation of quantum physics. Quantum mechanics is quite different from classical mechanics in that it abandons the ideas of particles, and precise measurement of the physical properties related to them. Rather, analyzes them in terms of probabilities.
It comes up with results that are hard to beleive but are experimentally found to be true.