Abstract
The theorem of Hohenberg and Kohn is extended to subdomains of a bounded quantum system. It is shown that the ground state particle density of an arbitrary subdomain uniquely determines the ground state properties of this subdomain, of any other subdomain, and of the total domain of the system.
Similar content being viewed by others
References
See e.g. Von Niessen, W.: J. Chem. Phys.55, 1948 (1971); Theoret. Chim. Acta (Berl.)31, 111 (1973); Theoret. Chim. Acta (Berl.)31, 297 (1973); Theoret. Chim. Acta (Berl.)32, 13 (1973); Peters, D.: J. Chem. Phys.67, 1284 (1977)
Bader, R. F. W.: Acct. Chem. Res.8, 34 (1975)
Srebrenik, S., Bader, R. F. W.: J. Chem. Phys.63, 3945 (1975); Bader, R. F. W., Runtz, G. R.: Mol. Phys.30, 117 (1975)
Srebrenik, S.: Intern. J. Quantum Chem. Symp.9, 357 (1975)
Srebrenik, S., Bader, R. F. W., Tung Nguyen-Dang, T.: J. Chem. Phys.68, 3667 (1978); Bader, R. F. W., Srebrenik, S., Tung Nguyen-Dang, T.: J. Chem. Phys.68, 3680 (1978); Bader, R. F. W., Tung Nguyen-Dang, T., Tal, Y.: J. Chem. Phys.70, 4316 (1979); Bader, R. F. W., Anderson, S. G., Duke, A. J.: J. Am. Chem. Soc.101, 1389 (1979) and references quoted in these papers
Hohenberg, P., Kohn, W.: Phys. Rev.136, B864 (1964)
Kato, T.: Trans. Am. Math. Soc.70, 195 (1951); Kato, T.: Communs. Pure and Appl. Math.10, 151 (1957); Ikebe, T., Kato, T.: Arch. Rat. Mech. Anal.9, 77 (1962)
Zislin, G. M.: Trud. Mosk. Mat. Obsc.9, 82 (1960)
Compare e.g. Theorem 7.5.1, in: Hörmander, L.: Linear partial differential operators, p. 178. Berlin: Springer-Verlag 1963
Bochner, S., Martin, W. T.: Several complex variables, Chapt. II, § 2, p. 33–34. Princeton: Princeton University Press 1948
Coleman, A. J.: Rev. Mod. Phys.35, 668 (1963), Theorem 9.3
Munch, W., Riess, J., Primas, H.: Rigorous proof of a theorem by Hohenberg and Kohn saying that quantum mechanical expectation values are unique functionals of the charge density, Lab. of Physical Chemistry, Swiss Federal Institute of Technology, Zurich (Switzerland), preprint (1967)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Riess, J., Münch, W. The theorem of hohenberg and kohn for subdomains of a quantum system. Theoret. Chim. Acta 58, 295–300 (1981). https://doi.org/10.1007/BF02426905
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02426905