What would it even mean for the coefficient to be higher than 1? At the seashore we see waves approaching the shore and they get larger as they arrive. transforms the other two equations into Airy differential equations: $$\frac{d^2\psi_{II}}{d\xi^2}=-\xi\psi_{II}$$ The reflection coefficient c may be positive or negative so the transmission coefficient t may be greater than unity. To learn more, see our tips on writing great answers. If a body explodes then Coefficient of restitution can be greater than 1. How should I consider a rude(?) Plotting $\psi$ for finite square well potential. I followed the method (see file CAL.png) but the results seems incorrect. Long story short, they list a Pearson coefficient of 1.802. @Sobanoodles: That's not what I mean. Has it something to do with the change of variables discussed in akhmeteli's answer and comments? For some wavelengths, the transmission coefficient is going above 1. $$\psi_{III}(x)=E\mathrm{Ai}(-\xi)+F\mathrm{Bi}(-\xi),$$. The currents are given by, $$J_I=\frac{\hbar}{m}\Im\left(\psi_I^*\frac{d\psi_I}{dx}\right)=\frac{\hbar}{m}(|A|^2-|B|^2)=J_{in}-J_{ref}$$ Use MathJax to format equations. Since I've got the Airy equation in the form $\frac{d^2\psi}{d\xi^2}+\xi\psi=0$, I've simply declared that the solutions are of the form $\psi(\xi)=K\mathrm{Ai}(-\xi)+J\mathrm{Bi}(-\xi),$ which is justified as a change of variables $\xi=-z$ in the conventional Airy equation $\frac{d^2\psi}{dz^2}-z\psi=0$. Should I discard the $T>1$ solutions and leave energy gaps in the graph? 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. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Thesis (M.S.) By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Does a metal have One, Zero or Infinite Relative Permittivity? 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. Wir würden gern zu Beginn dieses Kapitels die Frage „Was ist Elektrizität?“ mit einem ebenso knappen Kernsatz beantworten This type of work was a popular research topic in the 50-70s. 1D Scattering Phase Shift (Finite Well) - Unphysical? 0 & 0 & \mathrm{Ai}'(-\xi_0) & \mathrm{Bi}'(-\xi_0) & \mathrm{Ai}'(-\xi_0) & \mathrm{Bi}'(-\xi_0) \\ If not, then you have found a wave type propagation. 0 & 0 & \mathrm{Ai}(-\xi_0) & \mathrm{Bi}(-\xi_0) & -\mathrm{Ai}(-\xi_0) & -\mathrm{Bi}(-\xi_0) \\ The reflection coefficient c may be positive or negative so the transmission coefficient t may be greater than unity. Also see this article. For compressible flows, the pressure coefficient can be greater than 1. Why did you set (1,3), (1,4), (3,5) and (3,6) with -1 multiplier? Going by the definition of Coefficient of restitution, it is simply the ratio between relative velocities of particles before and after an interaction. E \\ $$\frac{d^2\psi_{III}}{dx^2}+(\frac{x}{a}+\epsilon^2-1)k_0^2\psi_{III}=0$$ Some initial substitutions: $k=\sqrt{\frac{2mE}{\hbar^2}}$, $k_0=\sqrt{\frac{2mV_0}{\hbar^2}}$, $q_0=(k_0a)^{2/3}$, $\epsilon^2=\frac{E}{V_0}$. This happens when you have a lossy transmission line with a complex termination. Or someone can show me how to write the input parameter. Ge^{ika} \\ Dose anyone know where to find some example ? I would suspect that your analytical solution does not satisfy the boundary conditions. Sometimes, as in this very case, our estimates of uncertainty can and should be improved, here T should be always contained in interval [0,1]. And the aim is to extract the acoustic reflection(A side)/transmission(B side) coefficients for the square zone in the green dashed-line frame. Why is the dielectric constant for metals infinity? I've edited the question now to show how I got to the graph, so you can see that I've set $\psi_{IV}=e^{ikx}$. Quite similarly, when almost nothing is transmitted and you register the noise only, it may happen that calculated transmission coefficient will become negative. Change $\psi_{IV}$ to $G e^{-i k x}$ I am working on a metal-dielectric geometry. C \\ In a waveguide or a fiber are TE-TM modes same as horizontal and vertical polarization? Sorry, i pressed enter and the page sent my brocken comment. At the seashore we see waves approaching the shore and they get larger as they arrive. then find --University of Arizona. Since $T+R=1$, it follows that $|A|^2-|B|^2=|G|^2$. You can choose values of parameters which will give transmission coefficients greater than 1, and that would appear to violate conservation of energy. In optics, transmission is the property of a substance to permit the passage of light, with some or none of the incident light being absorbed in the process. $$\frac{d^2\psi_{IV}}{dx^2}+k^2\psi_{IV}=0$$, Solutions to $I$ and $IV$ may be immediatly given as, $$\psi_I(x)=Ae^{ikx}+Be^{-ikx}$$ As far as I am aware, that isn't possible. Using the fact that both $\psi(x)$ and $\psi'(x)$ are continuous, this gives the linear system: $$\left(\begin{matrix} Axiomatic development of electrodynamics. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. 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 $x\to +\infty$? I know quantum espresso can calculate transport. Cutting out most sink cabinet back panel to access utilities. Leider geht das nicht: Während sich die Wärmelehre bruchlos in die Mechanik eingliedern lässt, ist Somehow you managed to transform this problem from triangle well to triangle barrier: Would you please elaborate that? Calculate the reflection probability instead \end{equation*}. What does it mean physically? Hi everybody, I am trying to retrieve, based on the acoustic reflection/transmission coefficients, the effective acoustic parameters of metametarials. Why Is an Inhomogenous Magnetic Field Used in the Stern Gerlach Experiment? When they are nearly equal, then the apparent result may easily exceed 1. What is the right way to calculating the acoustic reflection/transmission coefficients? incident wave . Using of the rocket propellant for engine cooling. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. What is the cost of health care in the US? If they travel less than a unit wavelength, then they are damped, evanescent waves. Reflection Coefficients … What is this part of an aircraft (looks like a long thick pole sticking out of the back)? 0 \\ Why is Soulknife's second attack not Two-Weapon Fighting?