The discretized Schrödinger equation is most often used to solve onedimensional quantum mechanics problems numerically. While it has been recognized for some time that this equation is equivalent to a simple tightbinding model and that the discretization imposes an underlying bandstructure unlike free-space quantum mechanics on the problem, the physical implications of this equivalence largely ...

The discretized Schrödinger equation is most often used to solve onedimensional quantum mechanics problems numerically. While it has been recognized for some time that this equation is equivalent to a simple tightbinding model and that the discretization imposes an underlying bandstructure unlike free-space quantum mechanics on the problem, the physical implications of this equivalence largely ...

We present the case of quantal transmission through a smooth, single-piece exponential potential, V (x) = −V0e x/a, in contrast to the piece-wise continuous potentials, as a pedagogic model to demonstrate the analytic extraction of transmission (reflection) co-efficient. The Schrödinger transmission through a one-dimensional potential well/barrier constitutes an essential topic in the courses a...

In the standard supernova picture, type Ib/c and type II supernovae are powered by the potential energy released in the collapse of the core of a massive star. In studying supernovae, we primarily focus on the ejecta that makes it beyond the potential well of the collapsed core. But, as we shall show in this paper, in most supernova explosions, a tenth of a solar mass or more of the ejecta is d...

Entangled states of composite quantum systems exhibit one of the most distinct and non-classical features of the quantum mechanical description of Nature, first pointed out by Schroedinger: ‘Maximal knowledge of a total system does not necessarily imply maximal knowledge of all its parts’. We provide an elementary illustration of this fundamental aspect of quantum physics by considering a syste...

of a bubble (F is the diele~tric onstant of liquid helium) gives the class~cal *'Coulomb radius" of the bubble (this value is accurate for the bubbles considered ( 5 , 6)). For typical charges Z of 10510' electrons, this yields radii between 10 and 100 pm. The electrons in a bubble are confined to a narrow region of only a fcw Bngstrorns width close to the bubble surface, owing to their mutual ...

We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (...