cragar said:When we setup the Schrodinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical.
Is this just a very good approximation or is there something subtle.
In quantum mechanics, the classical electric potential refers to the potential energy associated with the interaction between electric charges. It is a fundamental concept in understanding the behavior of electrically charged particles in quantum systems.
The classical electric potential is a continuous function that describes the interaction between electric charges, while the quantum mechanical potential is a discrete function that describes the probability of finding a particle in a certain location. Additionally, the classical electric potential follows the laws of classical mechanics, while the quantum mechanical potential follows the laws of quantum mechanics.
Approximating the classical electric potential in quantum mechanics allows us to simplify complicated quantum systems and make predictions about the behavior of electrically charged particles. It also helps us understand the connection between classical and quantum systems and how they relate to each other.
The classical electric potential is often approximated using the Born-Oppenheimer approximation, which separates the motion of the electrons from the motion of the nuclei. This allows us to treat the nuclei as classical particles and simplify the quantum mechanical calculations.
Exploring the approximation of classical electric potential in quantum mechanics has many practical applications, such as in the development of new materials, understanding chemical reactions, and designing electronic devices. It also plays a crucial role in the study of atomic and molecular systems in physics and chemistry.