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We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the allowed energies vary with the wells width and with the location of the delta function within it. The model subtly distinguishes between whether the delta function is located at rational or irrational fractions of the wells width: in the former case all possible energy eigenvalues are solutions to a straightforward dispersion relation, but in the latter case, to make up a complete set these `ordinary solutions must be augmented by the addition of `nodal states which vanish at the delta function and so do not `see it. Thus, although the model is a simple one, due to its singular nature it needs a little careful analysis. The model, of course, can be thought of as a limit of more physical smooth potentials which, though readily succumbing to straightforward numerical computation, would give little generic information. PACS numbers: 03.65.-w, 73.21.Fg, 01.40.-d
Domain walls arise in theories where there is spontaneous symmetry breaking of a discrete symmetry such as $mathbb{Z}_{N}$ and are a feature of many BSM models. In this work we consider the possibility of detecting domain walls through their optical
We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within the other. We focus on the fluctuation-induced pressure acting on the cavity wall, which is assumed to be spherical. This
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically enlarged. A
We study the real-time dynamics of a small bubble of false vacuum in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. Such a bubble can be thought of as a confi
Cardiovascular simulations are increasingly used for non-invasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due to input u