A wave packet is a group of waves that travel together as a single unit, rather than individually. It is also known as a localized wave, as it has a specific position and a finite size, unlike a plane wave which extends infinitely in space.
The physical reason for using wave packet expansion is that it allows us to describe the behavior of a particle with a well-defined position and momentum, unlike a plane wave which has a definite momentum but an indefinite position. This is important in understanding the dynamics of quantum systems.
Wave packet expansion is related to conservation laws through the conservation of energy and momentum. In a quantum system, the total energy and momentum of the particle are conserved, and the wave packet expansion allows us to calculate these values at any given point in time.
One limitation of wave packet expansion is that it assumes the particle's position and momentum are known with certainty, which is not always the case in quantum mechanics. Additionally, it does not take into account the effects of external forces, such as electromagnetic fields, on the particle.
Wave packet expansion can be applied to all types of waves, including electromagnetic waves, sound waves, and quantum waves. However, the specific mathematical form of the wave packet may differ depending on the type of wave and its properties.