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The formal foundation of TDDFT is the Runge–Gross (RG) theorem (1984) [1] – the time-dependent analogue of the Hohenberg–Kohn (HK) theorem (1964). [2] The RG theorem shows that, for a given initial wavefunction, there is a unique mapping between the time-dependent external potential of a system and its time-dependent density.
This theorem has since been extended to the time-dependent domain to develop time-dependent density functional theory (TDDFT), which can be used to describe excited states. The second HK theorem defines an energy functional for the system and proves that the ground-state electron density minimizes this energy functional.
The worked-example effect is a learning effect predicted by cognitive load theory. [1] [full citation needed] Specifically, it refers to improved learning observed when worked examples are used as part of instruction, compared to other instructional techniques such as problem-solving [2] [page needed] and discovery learning.
But Liouville's theorem does not imply that the ergodic hypothesis holds for all Hamiltonian systems. The ergodic hypothesis is often assumed in the statistical analysis of computational physics. The analyst would assume that the average of a process parameter over time and the average over the statistical ensemble are the same. This assumption ...
Theoretical psychology originated from the philosophy of science, with logic and rationality at the base of each new idea. It existed before empirical or experimental psychology. Theoretical psychology is an interdisciplinary field involving psychologists specializing in a wide variety of psychological branches.
The Cattell–Horn–Carroll theory is an integration of two previously established theoretical models of intelligence: the theory of fluid and crystallized intelligence (Gf-Gc) (Cattell, 1941; Horn 1965), and Carroll's three-stratum theory (1993), a hierarchical, three-stratum model of intelligence. Due to substantial similarities between the ...
Human performance modeling (HPM) is a method of quantifying human behavior, cognition, and processes.It is a tool used by human factors researchers and practitioners for both the analysis of human function and for the development of systems designed for optimal user experience and interaction . [1]
Like any mathematical model, expected utility theory simplifies reality. The mathematical correctness of expected utility theory and the salience of its primitive concepts do not guarantee that expected utility theory is a reliable guide to human behavior or optimal practice.