There are three expressions for the kinetic energy density t(r) expressed in terms of its quantal source, the single‐particle density matrix: tA(r), the integrand of the kinetic energy expectation value; tB(r), the trace of the kinetic energy tensor; tC(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.
M. Slamet and V. Sahni. Int. J. Quantum Chem. e25818 (2018).
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