scholarly journals Quantum Mechanical Reflection and Transmission Coefficients for a Particle through a OneDimensional Vertical Step Potential

2019 ◽  
Vol 8 (11) ◽  
pp. 2882-2886
Keyword(s):  
Laplace Transformation ◽  
Reflection And Transmission Coefficients ◽  
Quantum Mechanical ◽  
Mathematical Tool ◽  
Science And Engineering ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Vertical Step

In this paper, we illustrate an application of the Laplace transformation for finding the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Quantum mechanics is one of the branches of physics in which the physical problems are solved by algebraic and analytic methods. By applying the Laplace transformation, we can find the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Generally, the Laplace transformation has been applied in different areas of science and engineering and makes it easier to solve the problems inengineering applications. It is a mathematical tool which has been put to use for solving the differential equations without finding their general solutions. It has applications in nearly all science and engineering disciplines like analysis of electrical circuits, heat and mass transfer, fluid dynamics, nuclear physics, process controls, quantum mechanical problems,etc.

scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

scholarly journals A trace formula for schrödinger operators with step potentials

1982 ◽  
Vol 24 (2) ◽  
pp. 138-159 ◽  
Author(s):  
D. M. O'Brien
Keyword(s):  
Compact Support ◽  
Plane Waves ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Simple Step ◽  
Infinitely Differentiable Function

AbstractThis paper shows how to compute the trace of G(T) – G(T0), where G is an infinitely differentiable function with compact support, and where T and T0 are one-dimensional Schrödinger operators on (−∞, ∞) with potentials q and q0. It is assumed that q0 is a simple step potential and that q decays exponentially to q0. The trace is expressed in terms of the reflection and transmission coefficients for the scattering of plane waves by the potential q.

Evaluation of Moisture Content in Concrete with Microwave

2006 ◽  
Vol 312 ◽  
pp. 311-318 ◽  
Author(s):  
Xiao Ming Wang ◽  
Yinghao Teo ◽  
Wing K. Chiu ◽  
Greg Foliente
Keyword(s):  
Moisture Content ◽  
Water Content ◽  
Condition Monitoring ◽  
Reflection And Transmission Coefficients ◽  
Physical Change ◽  
Microwave Propagation ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Permittivity And Permeability

Generally, any chemical or physical change in a material may cause variation in its permittivity and permeability. The propagation of microwave through the material can be affected by these variation in properties. The analysis of microwave propagation through materials may therefore provide a means for condition monitoring. This paper utilizes a one-dimensional scenario, demonstrating the feasibility to link measurable reflection and transmission coefficients of microwave to concrete permittivity and permeability, which are essentially associated with water content in concrete. As a result, water content can then be monitored through the measurement of these coefficients. The study also demonstrates the feasibility of using the same technique to estimate the thickness of the concrete that microwave propagates through.

Data Processing for Corrections to the Two Potentials from the Generalized Uncertainty Principle

2014 ◽  
Vol 707 ◽  
pp. 386-389
Author(s):  
Zheng Huang
Keyword(s):  
Quantum Gravity ◽  
Data Processing ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Reflection And Transmission Coefficients ◽  
Quantum Mechanical ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Parabolic Potential ◽  
Quantum Phenomena

Various theories of Quantum Gravity predict the existence of a minimum observable length, or a maximum observable momentum, and the related generalized uncertainty principle (GUP), and it influences all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. The GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional toandrespectively, where is the GUP parameter. By considering both terms as perturbations .We compute such corrections to the two typical potentials: parabolic potential toand Dirac potential to. We show that the GUP affects reflection and transmission coefficients of the two potentials.

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