A trace formula for schrödinger operators with step potentials

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.

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

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.k2424.0981119 ◽

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.

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Reflection and Transmission Coefficients in Multi-Layered Fully Anisotropic Media Solved by Transfer Matrix Method with Plane Waves for Predicting Energy Transmission Course

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2020.3044591 ◽

2020 ◽

pp. 1-1

Author(s):

Yuxian Zhang ◽

Naixing Feng ◽

Guo Ping Wang ◽

Hongxing Zheng

Keyword(s):

Transfer Matrix ◽

Transfer Matrix Method ◽

Matrix Method ◽

Plane Waves ◽

Anisotropic Media ◽

Reflection And Transmission Coefficients ◽

Energy Transmission ◽

Reflection And Transmission ◽

Transmission Coefficients

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Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions

Communications in Mathematical Physics ◽

10.1007/bf02097231 ◽

1993 ◽

Vol 158 (1) ◽

pp. 45-66 ◽

Cited By ~ 82

Author(s):

Anton Bovier ◽

Jean-Michel Ghez

Keyword(s):

Spectral Properties ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional

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Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory

Annales Henri Poincaré ◽

10.1007/s00023-016-0543-0 ◽

2017 ◽

Vol 18 (6) ◽

pp. 2075-2085 ◽

Cited By ~ 1

Author(s):

Benjamin Landon ◽

Annalisa Panati ◽

Jane Panangaden ◽

Justine Zwicker

Keyword(s):

Scattering Theory ◽

Schrödinger Operators ◽

Schrodinger Operators ◽

One Dimensional

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Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials

Journal of Functional Analysis ◽

10.1016/j.jfa.2008.07.015 ◽

2008 ◽

Vol 255 (9) ◽

pp. 2321-2362 ◽

Cited By ~ 3

Author(s):

Ovidiu Costin ◽

Wilhelm Schlag ◽

Wolfgang Staubach ◽

Saleh Tanveer

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Semiclassical Analysis ◽

Zero Energy ◽

One Dimensional ◽

Energy Scattering ◽

Inverse Square Potentials

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Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

Journal of Vibration and Acoustics ◽

10.1115/1.2827388 ◽

2008 ◽

Vol 130 (3) ◽

Cited By ~ 12

Author(s):

J. Y. Chen ◽

H. L. Chen ◽

E. Pan

Keyword(s):

Piezoelectric Materials ◽

Plane Waves ◽

Layered Structures ◽

Organic Glass ◽

Reflection And Transmission Coefficients ◽

Material Structure ◽

Layered System ◽

Reflection And Transmission ◽

Transmission Coefficients ◽

Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

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