Two body problem of Hidrogen Atom

[torehan]

In Hidrogen atom, why we choose the center of mass coordinate which is on the same direction with relative coordinate?

 

[malawi_glenn]

the calculations become much much more simpler.

 

[denian]

The concept of the two body problem in the Hydrogen atom refers to the interaction between the positively charged nucleus (proton) and the negatively charged electron. This problem has been extensively studied in the field of quantum mechanics and is crucial in understanding the behavior of atoms.

In order to accurately describe the motion of the electron around the nucleus, we use a coordinate system that takes into account both the center of mass and relative coordinates. The center of mass coordinate is chosen to be on the same direction as the relative coordinate because it simplifies the mathematical equations involved in solving the problem.

Additionally, the center of mass coordinate takes into account the motion of both the electron and the nucleus, allowing us to accurately describe the motion of the system as a whole. This is important because the electron and nucleus are constantly in motion and their positions are constantly changing, making it necessary to consider both their individual motions as well as their combined motion.

Furthermore, the center of mass coordinate also helps in visualizing the system and understanding the distribution of mass and charge within it. By choosing a coordinate system that aligns with the relative motion of the two bodies, we can better understand how they interact and how their movements affect each other.

In conclusion, the choice of the center of mass coordinate being on the same direction as the relative coordinate in the Hydrogen atom is a practical and necessary approach in accurately describing and understanding the two body problem. It simplifies the mathematical equations, takes into account the motion of both bodies, and helps in visualizing the system.