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  2. Density functional theory - Wikipedia

    en.wikipedia.org/wiki/Density_functional_theory

    Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.

  3. Population balance equation - Wikipedia

    en.wikipedia.org/wiki/Population_balance_equation

    Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r corresponds to spatial position or external coordinates) dispersed in a continuous phase defined by a phase vector Y(r,t) (which again is a function of all such vectors which ...

  4. Diffusion equation - Wikipedia

    en.wikipedia.org/wiki/Diffusion_equation

    where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.

  5. Ab initio quantum chemistry methods - Wikipedia

    en.wikipedia.org/wiki/Ab_initio_quantum...

    The problem of computational expense can be alleviated through simplification schemes. [7] In the density fitting scheme, the four-index integrals used to describe the interaction between electron pairs are reduced to simpler two- or three-index integrals, by treating the charge densities they contain in a simplified way. This reduces the ...

  6. Quantum master equation - Wikipedia

    en.wikipedia.org/wiki/Quantum_master_equation

    A quantum master equation is a generalization of the idea of a master equation.Rather than just a system of differential equations for a set of probabilities (which only constitutes the diagonal elements of a density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements.

  7. Kohn–Sham equations - Wikipedia

    en.wikipedia.org/wiki/Kohn–Sham_equations

    In physics and quantum chemistry, specifically density functional theory, the Kohn–Sham equation is the non-interacting Schrödinger equation (more clearly, Schrödinger-like equation) of a fictitious system (the "Kohn–Sham system") of non-interacting particles (typically electrons) that generate the same density as any given system of interacting particles.

  8. Master equation - Wikipedia

    en.wikipedia.org/wiki/Master_equation

    A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical. Off-diagonal elements represent quantum coherence which is a physical characteristic that is intrinsically quantum mechanical.

  9. Mass concentration (chemistry) - Wikipedia

    en.wikipedia.org/wiki/Mass_concentration_(chemistry)

    In chemistry, the mass concentration ρ i (or γ i) is defined as the mass of a constituent m i divided by the volume of the mixture V. [1]= For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture.

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