georg gill said:
The Kohn Hohenberg theorem is a fundamental result in quantum mechanics that provides a way to calculate the ground-state energy and density of a many-body system based on the external potential. It states that the ground-state energy and density of a system are uniquely determined by the external potential, and vice versa.
The Kohn Hohenberg theorem is significant because it allows for the practical calculation of the ground-state properties of a many-body system, which would otherwise be extremely difficult to obtain. It also provides a rigorous mathematical framework for understanding the relationship between the external potential and the properties of the system.
The original Kohn Hohenberg theorem only applies to systems with a unique ground state, while the extended version applies to systems with degenerate ground states. The extended theorem also allows for the inclusion of constraints, such as spin polarization, in the calculation of the ground-state density.
The Kohn Hohenberg theorem has numerous applications in theoretical chemistry and condensed matter physics, such as in the calculation of electronic structure and the prediction of material properties. It is also used in the development of density functional theory, a widely used computational method in quantum chemistry.
While the Kohn Hohenberg theorem is a powerful tool for understanding many-body systems, it does have some limitations. It only applies to systems at absolute zero temperature, and it assumes that the external potential is fixed and does not change in response to the particle density. It also does not take into account quantum fluctuations, which can be important in some systems.