What is reduced mass?

Reduced mass is a concept in physics and is used to describe the effective mass of two or more objects when they are in motion relative to each other. It is particularly relevant in systems with multiple interacting particles, such as atoms and molecules.

Reduced mass is calculated as the inverse of the sum of the reciprocals of the masses of the individual objects. For a system of two objects with masses m1 and m2, the reduced mass can be calculated as:

1/(1/m1 + 1/m2)

The reduced mass is used in the context of the two-body problem in classical mechanics and quantum mechanics. In a system of two objects, the reduced mass represents the mass that moves in response to the force applied to the entire system.

For example, in the case of a hydrogen atom composed of a proton and an electron, the reduced mass is calculated using the masses of the proton and electron, since both particles are in motion relative to each other.

Overall, reduced mass provides a way to simplify the analysis of complex systems by considering the motion of the system as a whole rather than the individual masses of the constituent objects.