Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

Virtue, Law and Mercy

The attribution of responsibility in world society is increasingly a field of contestation. On the one hand, the perception of causal and moral links reaching far in space and time are ever more explicitly pronounced; on the other hand, the very complexity of these links often engenders a fragmentation of responsibility both in law (Veitch 2007) as well as in moral commitment. Moreover, those institutions of legal responsibility attempting to reflect some of these interrelations are often criticised as insufficient by those who follow alternative narratives of causation and moral community. Current institutions of responsibility in law appear to abstract from what could be called enabling contexts; they perform their cuts in the chains of enabling interactions at very brief intervals (Strathern 2001). The result is often “organised irresponsibility” (Veitch 2007; Beck 1996), producing appeals to a global community of concern in time and space without corresponding obligatory commitments. This talk explores alternative conceptualisations of responsibility, and enquires into their notion of the person, their temporal and socio-spatial dimensions, and their notion of liability.