The quantum mechanical hypervirial theorems (HVT) technique is used in treating two basic inequalities relating the ground-state mean square radius of the orbit of a particle in a central potential and its kinetic energy, respectively, to the spacing of the two lowest energy levels Δ E . For quite a wide class of those potentials, the parameters of which also lead to a sufficiently small dimensionless quantity s , the difference between the two sides of each inequality is of order s 3 and higher (while Δ E is of order s and higher), and thus it is expected in general to be quite small.The quantum mechanical hypervirial theorems (HVT) technique is used in treating two basic inequalities relating the ground-state mean square radius of the orbit of a particle in a central potential and its kinetic energy, respectively, to the spacing of the two lowest energy levels Δ E . For quite a wide class of those potentials, the parameters of which also lead to a sufficiently small dimensionless quantity s , the difference between the two sides of each inequality is of order s 3 and higher (while Δ E is of order s and higher), and thus it is expected in general to be quite small.

Journal of Physics A Mathematical and GeneralFeb 25, 20022 citations

One- and Two-Particle Systems in Three Dimensions

Springer eBooksMar 31, 20060 citations

Towards a Particle Theory in Two Dimensions

Laurens Vanderstraeten

Springer thesesJan 1, 20171 citation

Density-functional theory for two noninteracting spinless fermions

F. Aryasetiawan, Malcolm J. Stott

A method is presented for relating a ground-state density distribution to the effective single-particle potential which has this density for its ground state for a noninteracting system of particles. The method is useful for systems consisting of a small number of spinless fermions and in the case of two particles a second-order, nonlinear differential equation relates the density and the effective potential. The question of $v$ representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state $v$ representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.A method is presented for relating a ground-state density distribution to the effective single-particle potential which has this density for its ground state for a noninteracting system of particles. The method is useful for systems consisting of a small number of spinless fermions and in the case of two particles a second-order, nonlinear differential equation relates the density and the effective potential. The question of $v$ representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state $v$ representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.

Physical review. B, Condensed matterSep 15, 198648 citations

Free Particle Motion in Three Dimensions

S. Brandt, Hans Dieter Dahmen, Tilo Stroh

Springer eBooksNov 26, 20100 citations

Real-space diffusion theory of multiparticle quantum systems

Marvin McClendon

A three-dimensional stochastic process which has the particle density as its probability density is constructed from Nelson's stochastic mechanics, yielding a particle trajectory picture for density-functional theory. This diffusion process enables simulating the detailed behavior of multiparticle quantum systems with substantial computational economy. A stochastic-mechanical form of the Heisenberg uncertainty principle holds in the new context. Moreover, a kinetic energy functional is defined and shown to be connected with other kinetic energy expressions, and in the case of a time-independent ground state a formal dynamics for the process is proposed. A related real-space version is developed of Bohm's quantum potential formalism.A three-dimensional stochastic process which has the particle density as its probability density is constructed from Nelson's stochastic mechanics, yielding a particle trajectory picture for density-functional theory. This diffusion process enables simulating the detailed behavior of multiparticle quantum systems with substantial computational economy. A stochastic-mechanical form of the Heisenberg uncertainty principle holds in the new context. Moreover, a kinetic energy functional is defined and shown to be connected with other kinetic energy expressions, and in the case of a time-independent ground state a formal dynamics for the process is proposed. A related real-space version is developed of Bohm's quantum potential formalism.

Physical Review ADec 1, 19888 citations

v

representability is addressed through examples of densities for one- and three-dimensional systems. It is found that densities of the form ${e}^{\ensuremath{-}ar}$ for two-particle systems are not ground-state

v

representable. The added flexibility of three dimensions over one allows an effective potential which does not necessarily have the chosen density as its ground state, but as its lowest nondegenerate state.