An energy eigenstate is a state in which a particle has a definite energy value. In other words, it is a state in which the particle's energy can be measured with certainty.
A particle in an energy eigenstate does not move because it is in a state of equilibrium. Its energy is constant and there is no net force acting on it, so it remains stationary.
The significance of a particle being in an energy eigenstate is that it allows for precise calculations and measurements of its energy. This is important in many areas of physics, such as quantum mechanics and thermodynamics.
Yes, a particle in an energy eigenstate can change to a moving state if it interacts with another particle or if an external force is applied to it. However, it will still have a definite energy value.
The uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle. In the case of a particle in an energy eigenstate, its energy is known with certainty, so the uncertainty lies in its position and momentum. This means that while the particle may not be moving, its exact position cannot be determined.