Speaker : Prof . Rajeev K . Pathak Department of Physics , University of Pune , India Time : 4 pm on Thursday

In quantum mechanics, the wave function embodies all the information that can be pragmatically extracted from a system. However, for a many-electron system, it is not the wave function, but it is rather the electron density that is observable by direct experimentation (for example, coherent and elastic XRay scattering). The coordinate electron density’s momentum-space analogue, viz. the electron momentum density is tangible through an inelastic process, viz. Compton scattering. While the many-electron wave function in coordinate and momentum spaces are connected by a manyparticle Fourier transformation, the densities bear no such (direct or indirect) connection. To reiterate Pauli’s eloquent remark verbatim: “...because God hath rent them asunder...!” There is no ‘phase-space’ in quantum mechanics with finer representation of states below the limit permissible by the uncertainty principle. We present a scheme to bridge the two canonically conjugate spaces of coordinates and momenta, without any explicit use of many-electron wave functions. First, we employ a quasi-classical approach, leading to an atomic density-functional model. Subsequently, we invoke an ingenious variant of the Density Functional Theory, viz. the Zhao-Parr-Morrison construction which ‘transforms’ the coordinate space density to its momentum space counterpart. We present some ‘exotic’ interconnections amongst seemingly unrelated physical quantities in the two spaces.