The term "degree of freedom" refers to the independent ways in which a particle can move or vibrate in a given system. In particle physics, it is used to describe the number of ways in which a particle can move or rotate in a specific direction.
In a system with N particles, there are 3N possible degrees of freedom. This means that each particle has three independent ways in which it can move or rotate in space, giving a total of 3N degrees of freedom for the entire system.
The degree of freedom is important because it determines the amount of energy that a particle can possess. In general, the more degrees of freedom a particle has, the more energy it can have. This is crucial in understanding the thermodynamic properties of a system, such as temperature and pressure.
The 3N dof rule applies to both classical and quantum systems, but with some differences. In classical systems, the particles are treated as point masses and the 3N degrees of freedom refer to their translational and rotational motions. In quantum systems, the particles are described by wave functions and the 3N degrees of freedom refer to the different quantum states that a particle can occupy.
Yes, the number of degrees of freedom can change in a given system. For example, if a bond is broken between two particles, there will be one less degree of freedom in the system. Additionally, in certain cases such as phase transitions, the number of degrees of freedom can change as the system undergoes a change in state.