Path distributions for describing eigenstates of the harmonic oscillator and other 1-dimensional problems

The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an integral expression is written that describes the wave function. This expression conventionally takes the form of an integral over initial locations of a particle, but it is re-expressed here in terms of a characteristic momentum associated with motion between the endpoints of a path. In this manner, the resulting expression can be analyzed using a generalization of stationary-phase analysis, leading to distributions of paths that exactly describe each eigenstate. These distributions are valid for all travel times, but when evaluated for long times they turn out to be real, non-negative functions of the characteristic momentum. For the harmonic oscillator in particular, a somewhat broad distribution is found, peaked at value of momentum that corresponds to a classical energy which in turn equals the energy eigenvalue for the state being described.Comment: 26 page, 10 figures; in v2, added refs. 43 and 44 along with a brief description of the latter, and made a few minor typographical correction

SymFET: A Proposed Symmetric Graphene Tunneling Field Effect Transistor

In this work, an analytical model to calculate the channel potential and current-voltage characteristics in a Symmetric tunneling Field-Effect-Transistor (SymFET) is presented. The current in a SymFET flows by tunneling from an n-type graphene layer to a p-type graphene layer. A large current peak occurs when the Dirac points are aligned at a particular drain-to- source bias VDS . Our model shows that the current of the SymFET is very weakly dependent on temperature. The resonant current peak is controlled by chemical doping and applied gate bias. The on/off ratio increases with graphene coherence length and doping. The symmetric resonant peak is a good candidate for high-speed analog applications, and can enable digital logic similar to the BiSFET. Our analytical model also offers the benefit of permitting simple analysis of features such as the full-width-at-half-maximum (FWHM) of the resonant peak and higher order harmonics of the nonlinear current. The SymFET takes advantage of the perfect symmetry of the bandstructure of 2D graphene, a feature that is not present in conventional semiconductors