Study of the kinetic energy densities of electrons as applied to quantum dots in a magnetic field

Abstract

There are three expressions for the kinetic energy density t(r) expressed in terms of its quantal source, the single‐particle density matrix: t A(r), the integrand of the kinetic energy expectation value; t B(r), the trace of the kinetic energy tensor; t C(r), a virial form in terms of the ‘classical’ kinetic field. These kinetic energy densities are studied by application to ‘artificial atoms‘ or quantum dots in a magnetic field in a ground and excited singlet state. A comparison with the densities for natural atoms and molecules in their ground state is made. The near nucleus structure of these densities for natural atoms is explained. We suggest that in theoretical frameworks which employ the kinetic energy density such as molecular fragmentation, density functional theory, and information‐entropic theories, one use all three expressions on application to quantum dots, and the virial expression for natural atoms and molecules. New physics could thereby be gleaned.

The ‘Quantal Newtonian’ First Law: A Complementary Perspective to the Stationary‐state Quantum Theory of Electrons

“…In a manner similar to Newton's First Law of Eq. ( 12), the statement of the QNFL is that the sum of the external and internal fields experienced by each electron vanishes: (Units of ), (20) As in classical physics (Eq. ( 13)), the external field is comprised of the sum of the electrostatic and Lorentz fields: (21) The internal field of the QNFL differs from that of classical physics (Eq.…”

“…(The expression for the kinetic energy T of Eq. ( 26) is the third expression in the literature [20] for the kinetic energy density as obtained from the single-particle density matrix . This should be of value in Kohn-Sham [16] density functional theory (see e. g., [21,22] and work [23][24][25] in which information-entropic measures are used within quantum mechanics.…”

New Perspectives on the Schr{ö}dinger-Pauli Theory of Electrons: Part II: Application to the Triplet State of a Quantum Dot in a Magnetic Field

“…and a = r − r. The operators  and B are Hermitian. The single-particle density matrix is the quantal source for all kinetic related properties [22] such as the kinetic energy tensor, the kinetic energy density, the kinetic field, the kinetic energy, and as noted above, the paramagnetic current density.…”