Related papers: Constraining transmission and reflection probabili…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
In this paper, we analyze, by using a matrix approach, the dynamics of a non-relativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schrodinger equation allows to obtain a…
A class of models is considered for a quantum particle constrained on degenerate Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the underlying geometry: the corresponding spectral analysis is developed in…
Herein, the canonical Fowler-Nordheim theory is extended by computing the zero-temperature transmission probability for the more general case of a barrier described by a fractional power law. An exact analytical formula is derived, written…
It was found recently that tunneling probabilities over a barrier is roughly twice as large as that given by standard WKB formula. Here we explained how this come from and showed that WKB method does give a good approximation over almost…
In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of non-rotating black holes are also modified. In this paper we ask: can these modifications be constrained with…
Photodetachment of H$^-$ near a potential barrier is studied. A new formula is presented for the cross sections induced by a barrier. The new formula describes two quantum effects near barrier tops. For energies near and above barrier tops,…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
Exactly solvable models are interesting for science and education, since they help in scientific search and in understanding of phenomena. Some exact solutions for simple quantum-mechanical models are considered. The models include two…
In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point…
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…
In this paper, we calculate the transmission and reflection amplitudes of wave functions for different potentials such as the delta function, the rectangular barrier, the Eckart potential, and the Hulthen potential. We describe the…
Liouville transformations map in a rigorous manner one Schr\"odinger equation into another, with a changed scattering potential. They are used here to transform quantum reflection of an atom on an attractive well into reflection of the atom…
We numerically integrate the time-dependent Schrodinger equation in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We find that linear superpositions of the basis states, with…
By directly integrating the Schroedinger starting in the transmission region and working backwards through the barrier, the tunneling probability can be determined for arbitrary potential barriers. The method employs techniques familiar to…