%'e calculate the diamagnetic susceptibility of a uniform interacting electron gas in the random-phase approximation.From this the exact high-density expansion of the diamagnetic susceptibility is obtained.

In this paper, we solve the Schrödinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schrödinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting timedomain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems.

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

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