tailieunhanh - Nano - and Micro Eelectromechanical Systems - S.E. Lyshevski Part 7

Tham khảo tài liệu 'nano - and micro eelectromechanical systems - . lyshevski part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | electrons per unit volume function of three spatial variables x y and z in the Cartesian coordinate system . The quantum mechanics and quantum modeling must be applied to understand and analyze nanostructures and nanodevices because they operate under the quantum effects. The total energy of N-electron system under the external field is defined in the term of the three-dimensional charge density p r 1 - 5 . The complexity is significantly decreased because the problem of modeling of N-electron Z-nucleus systems become equivalent to the solution of equation for one electron. The total energy is given as E t p r ri t p r r t p r f p r dr kinetic energy R 4rn r - r I potential energy where ri t p r and r2 t p r are the interacting exchange and noninteracting kinetic energies of a single electron in N-electron Z-nucleus system r t p r J 7 t p r p r dr r2 t p r - - y f t r Vfyj t r dr R 2m R Y t p r is the parameterization function. It should be emphasized that the Kohn-Sham electronic orbitals are subject to the following orthogonal condition JV t r j t r dr 8j . R The state of substance media depends largely on the balance between the kinetic energies of the particles and the interparticle energies of attraction. The expression for the total potential energy is easily justified. f ep r . . Term J 4 I 1 dr represents the Coulomb interaction in R and the total potential energy is a functions of the charge density p r . The total kinetic energy interactions of electrons and nuclei and electrons is integrated into the equation for the total energy. The total energy as given by is stationary with respect to variations in the charge density. The charge density is found taking note of the Schrodinger equation. The first-order Fock-Dirac electron charge density matrix is N pe r x t r j t r . j i The three-dimensional electron charge density is a function in three variables x y and z in the Cartesian coordinate system . Integrating the electron charge .

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