I've found this as a related question, but I'm not really satisfied with the answers. $$\frac{d^2\psi_{III}}{dx^2}+(\frac{x}{a}+\epsilon^2-1)k_0^2\psi_{III}=0$$ Does a metal have One, Zero or Infinite Relative Permittivity? Apparently it is also possible that you have designed a "metamerial" which gain their unusual properties due to structural arrangements. coefficient as Define transmission coefficient as . Please help us. I was recently reading this study. Now, I've gone over my calculations a dozen times, and I still can't spot a mistake, so I want to know wheather it's possible to have a transmission coefficient greater than one for certain values of energy, like in this scenario. Now, I've gone over my calculations a dozen times, and I still can't spot a mistake, so I want to know wheather it's possible to have a transmission coefficient greater than one for certain values of energy, like in this scenario. Quite similarly, when almost nothing is transmitted and you register the noise only, it may happen that calculated transmission coefficient will become negative. $\begingroup$ Autoregressive parameters can be greater than 1 but sometimes there are constraints on the coefficients when stationarity is required or if the process should not be explosive. Quick link too easy to remove after installation, is this a problem? Calculate the reflection probability instead 0 \\ We are not able to install and run the softare. I am completely not sure if this is significant for your problem. --University of Arizona. F If your transmission coefficient is the ratio of amplitudes then, Institute of Physics of the Polish Academy of Sciences. I've edited the question now to show how I got to the graph, so you can see that I've set $\psi_{IV}=e^{ikx}$. I'm trying to find the reflection and transmission coefficients for a stream of electrons coming from $x=-\infty$ (so $E>0$, no bound states involved). In order to do that, I've divided the domain into 4 parts (like in the picture), solved the Schrödinger equation on each one, got a linear system for the coefficients of each wavefunction and solved it. Is Elastigirl's body shape her natural shape, or did she choose it? $G$ is actually undetermined and is used as a free coefficient (every other coefficient can be expressed as $L=G\cdot blabla$), so it may be freely set to be 1. It may seem surprising that t can be greater than unity. As far as I am aware, that isn't possible. It might be due to propagation and attenuation characteristics of the waves in that medium. Use MathJax to format equations. Can the President of the United States pardon proactively? Obtaining Transmission Coefficient of Beam Upon a Linear Potential, QM: Finite Potential Square Well Solved without Symmetry Assumption, Transmission coefficient of a Gaussian wave packet through a potential barrier, Title of book about humanity seeing their lives X years in the future due to astronomical event, What would result from not adding fat to pastry dough, What modern innovations have been/are being made for the piano. 0 \\ $\begingroup$ A laser amplifier has a transmission coefficient greater than 1 (aka gain), for some range of wavelengths. In such cases, how do you define transmission coefficient? What is the right way to calculating the acoustic reflection/transmission coefficients? \end{matrix} \right) $$, where \xi_a\equiv\xi(x=a)=\xi(-a)=q_0\epsilon^2 and \xi_0\equiv\xi(0)=q_0(\epsilon^2-1) appear as shorthand notations. (See model.jpg) The white rectangle is a solid structure impinged by plane acoustic wave from the left port, while a plane wave radiation condition is assigned to the right end. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Leider geht das nicht: Während sich die Wärmelehre bruchlos in die Mechanik eingliedern lässt, ist Didn't you forget to set a condition which reflects the fact that there is no incoming particles from the right, that is, the amplitude of the phase e^{-ixk} is zero for x\to +\infty? Cutting out most sink cabinet back panel to access utilities. Why is Soulknife's second attack not Two-Weapon Fighting? Does anybody know how obtaining free licence of ATK-VNL software? I've played with other values of a and V_0 as well, and the issue of T>1 persists, if that's what you mean. Asking for help, clarification, or responding to other answers. At the seashore we see waves approaching the shore and they get larger as they arrive. More seriously: your transmission coefficient is a ratio of two uncertain (noisy) quantities. Why Is an Inhomogenous Magnetic Field Used in the Stern Gerlach Experiment? The solution of the Airy equation bifurcates depending on whether you have -k^2 or +k^2 (in notation of, @akhmetali I see what you mean. the first corresponding to the incoming and reflected wave, and the other to the transmitted wave. You have to specify how you arrive at this T>1 result and give some pertinent formulas.$$\frac{d^2\psi_{III}}{d\xi^2}=-\xi\psi_{III}$$,$$\psi_{II}(x)=C\mathrm{Ai}(-\xi)+D\mathrm{Bi}(-\xi)$$Since T+R=1, it follows that |A|^2-|B|^2=|G|^2. Includes bibliographical references. All was well untill I plugged the analytic solution for the transmission coefficient into Python to render a graph and got this. About trianlge barrier: in the well: k^2=\frac{2m(E-V)}{\hbar^2} = \frac{2mV_0}{\hbar^2}(\frac{E}{V_0}-\frac{|x|}{a}+1)=k_0^2(\epsilon^2-\frac{|x|}{a}+1) so you must rewrite equations for \psi_{II} and \psi_{III}. EDIT: The comments suggest to give an insight into my analytical solution. (For example, try light incident from a medium of n 1 =1.5 upon a medium of n 2 =1.0 with an angle of incidence of 30°.) Somehow you managed to transform this problem from triangle well to triangle barrier: Would you please elaborate that? 0 \\ Or someone can show me how to write the input parameter. Prime corresponds to \frac{d}{dx}. Why are Stratolaunch's engines so far forward? Sometimes the reflection / transmission coefficient may be slightly greater than 1. Also did you mention that for one of \psi_{II} and \psi_{III} : \frac{d}{dx} = \frac{d}{d\xi} and for the other \frac{d}{dx} = -\frac{d}{d\xi}, Meaning of transmission coefficient greater than one in a potential well problem, mathworld.wolfram.com/AiryDifferentialEquation.html, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. When are they same when are they different? Thanks for contributing an answer to Physics Stack Exchange! Yes. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. E is in eV, x and a in nm. Making statements based on opinion; back them up with references or personal experience. 0 & 0 & \mathrm{Ai}'(-\xi_0) & \mathrm{Bi}'(-\xi_0) & \mathrm{Ai}'(-\xi_0) & \mathrm{Bi}'(-\xi_0) \\ I am working on a metal-dielectric geometry. Going by the definition of Coefficient of restitution, it is simply the ratio between relative velocities of particles before and after an interaction. Help us to install and run Boltztrap 1.2.5 software. &\left.-\left(\left(\frac{ka}{q_0}\right)^2\mathrm{Ai}(-\xi_a)\mathrm{Bi}(-\xi_a)+\mathrm{Ai}'(-\xi_a)\mathrm{Bi}'(-\xi_a)\right)(\mathrm{Ai}(-\xi_0)\mathrm{Bi}'(-\xi_0)+\mathrm{Ai}'(-\xi_0)\mathrm{Bi}(-\xi_0)) \right], Reflection coefficient, r 1.0.5 0-.5-1.0 r || r ┴ 0° 30° 60° 90° Brewster’s angle Total internal reflection Critical angle Critical angle Total internal reflection above the "critical angle" crit sin-1(n t /n i) 41.8° for glass-to-air n glass > n air (The sine in Snell's Law can't be greater than one!) incident wave . 0 & 0 & 0 & 0 & \mathrm{Ai}'(-\xi_a) & \mathrm{Bi}(-\xi_a) Factorising Harder Quadratics Revision Notes. I'm aware that this breaks conservation of energy (red alert! C \\ © 2008-2020 ResearchGate GmbH. In case of few heterostructure problem, the transmission vs fermi energy curve shows more than 1. what does it signify? The classic case of having activity coefficient greater than 1 is the solution of very hydrophobic organic solvents in water. The reflection coefficient c may be positive or negative so the transmission coefficient t may be greater than unity. The penetration depth of the wave is not determined by the amplitude alone. I've tried V_0=0, but the algorhitm crashes because somewhere a division with zero occurs (since A\propto V_0).$$\frac{d^2\psi_{II}}{dx^2}+(-\frac{x}{a}+\epsilon^2-1)k_0^2\psi_{II}=0 \end{matrix} \right)\left(\begin{matrix} e^{-ika} & e^{ika} & -\mathrm{Ai}(-\xi_a) & -\mathrm{Bi}(-\xi_a) & 0 & 0 \\ -\frac{ika}{q_0}e^{-ika} & \frac{ika}{q_0}e^{ika} & \mathrm{Ai}'(-\xi_a) & \mathrm{Bi}'(-\xi_a) & 0 & 0 \\ I haven't studied your solution in detail, but, for what it's worth, the formulas for the solutions of Airy equation differ depending on the sign of the coefficient. Maths revision video and notes on the topic of factorising quadratics with a coefficient of x squared greater than one. If not, then you have found a wave type propagation. For example, if you have toluene or benzene in water, these molecules do not prefer to stay in water.

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