All was well untill I plugged the analytic solution for the transmission coefficient into Python to render a graph and got this. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The reflection coefficient c may be positive or negative so the transmission coefficient t may be greater than unity. In a waveguide or a fiber are TE-TM modes same as horizontal and vertical polarization? You can choose values of parameters which will give transmission coefficients greater than 1, and that would appear to violate conservation of energy. --University of Arizona. Help us to install and run Boltztrap 1.2.5 software. where $\mathrm{Ai}(z)$ and $\mathrm{Bi}(z)$ are the standard Airy functions of the first and second kind. How to install and run Boltztrap 1.2.5 freely downloadable from internet? 0 \\ Use MathJax to format equations. If R 0 equals 1, each existing infection causes one new infection. -\frac{ika}{q_0}e^{-ika} & \frac{ika}{q_0}e^{ika} & \mathrm{Ai}'(-\xi_a) & \mathrm{Bi}'(-\xi_a) & 0 & 0 \\ It's nothing to be alarmed about. If your transmission coefficient is the ratio of power in to power out then Marek's answer is correct, unless you have a medium or boundary with gain (e.g. If some light is absorbed by the substance, then the transmitted light will be a combination of the wavelengths of the light that was transmitted and not absorbed. So maybe you should give the details of your analytical solution, otherwise it is difficult to say anything for sure. Not a surprise. Why is Soulknife's second attack not Two-Weapon Fighting? This is one more example that the raw result of measurement, without estimated uncertainty ("error bounds") is next to worthless. Should I discard the $T>1$ solutions and leave energy gaps in the graph? It only takes a minute to sign up. 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). If white light is shone through the filter, the light transmitted also appears blue because of the absorption … We are not able to install and run the softare. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Reflection Coefficients … Does a metal have One, Zero or Infinite Relative Permittivity? $$\frac{d^2\psi_{III}}{dx^2}+(\frac{x}{a}+\epsilon^2-1)k_0^2\psi_{III}=0$$ \end{matrix} \right)=\left( \begin{matrix} $$\frac{d^2\psi_{III}}{d\xi^2}=-\xi\psi_{III}$$, $$\psi_{II}(x)=C\mathrm{Ai}(-\xi)+D\mathrm{Bi}(-\xi)$$ e^{-ika} & e^{ika} & -\mathrm{Ai}(-\xi_a) & -\mathrm{Bi}(-\xi_a) & 0 & 0 \\ The reflection coefficient of any device (S11), can it be greater than one? What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? I was recently reading this study. At the seashore we see waves approaching the shore and they get larger as they arrive. \end{split} If your transmission coefficient is the ratio of power in to power out then Marek's answer is correct, unless you have a medium or boundary with gain (e.g. Eine der vier fundamentalen Wechselwirkungskräfte ist die elektromagnetische Wechselwirkungskraft. Asking for help, clarification, or responding to other answers. Using of the rocket propellant for engine cooling. 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]. What would it even mean for the coefficient to be higher than 1? This does not violate any physical laws. $$\psi_{IV}(x)=Ge^{ikx},$$. 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. It also needs to be pumped (energy put in) to amplify the beam. $\begingroup$ A laser amplifier has a transmission coefficient greater than 1 (aka gain), for some range of wavelengths. reply from a potential PhD advisor? See this, National Institute of Science Education and Research. Long story short, they list a Pearson coefficient of 1.802. Leider geht das nicht: Während sich die Wärmelehre bruchlos in die Mechanik eingliedern lässt, ist This does not violate any physical laws. Should we leave technical astronomy questions to Astronomy SE? What confuses me more is the sings of the elements in your matrix. Meanwhile I've also solved the problem numerically, and got pretty expected results, like the one below. C \\ What is the right way to calculating the acoustic reflection/transmission coefficients? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. \begin{equation*}\label{parametara} MathJax reference. 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. D \\ Is there anyone can help me with this, thanks. \begin{split} I would suspect that your analytical solution does not satisfy the boundary conditions. Has it something to do with the change of variables discussed in akhmeteli's answer and comments? F How do I figure out the probability of finding a particle between two barriers? Have you checked that your solutions are applicable independent of the value of $E$? When they are nearly equal, then the apparent result may easily exceed 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…. That seems pretty arbitrary arbitrary to me, but it may be the case here. In such cases, how do you define transmission coefficient? -G\frac{ika}{q_0}e^{ika} We have downloaded Boltztrap 1.2.5 from internet. For compressible flows, the pressure coefficient can be greater than 1. $\endgroup$ – Jon Custer Jul 25 '16 at 12:55 Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. that should work well. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. If your transmission coefficient is the ratio of amplitudes then, Institute of Physics of the Polish Academy of Sciences. Or someone can show me how to write the input parameter. Reflectivity and transmissivity greater than 1. Here are three different methods for factorising harder quadratics, you only need to know one of them.

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