Transmission coefficient Definition and 36 Threads

In a) I get that T should be largest where V_0 is least wide, because when V_0 is infinitely wide the particle would be fully reflected. But I don't get how height in b) and energy levels height in c) correlates to T and R. Is it because of their k? I get the opposite answer from the correct...

Initially '0' is the upper limit and ##a = \frac{Ze^2}{E}## is the lower limit. With change of variable ##x = \frac{Er}{Ze^2}##, for ##r=0##, ##x=0##, and for ##r=\frac{Ze^2}{E}##, ##x=1##, so 1 should be the lower limit. However, he takes 1 as the upper limit, and without a minus sign. Why is...

How did you find PF?: Google search I got a problem, how to calculate this formula from euler to imajiner? or how calculate this case?

Homework Statement: The Task is to calculate the Transmission coefficient with the WKB Approximation of following potential: V(x) = V_0(1-(x/a)²) |x|<a ; V(x) = 0 otherwise Homework Equations: ln|T|² = -2 ∫ p(x) dx I have inserted the potential in the equation for p(x) and recieved p(x) =...

Diagram Calculations as follows $$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{I_{R_1}+I_{R_2}}{I_0}*100=\frac{R*I_0+(R*T)*I_0}{I_0}$$ Subbing in the relevant equations given in the question $$\frac{I_{total \...

The Hamiltonian of the system I'm working on is in the form : ##\hat H=\dfrac{p^2}{2m}-\dfrac{\partial_z^2}{2m}+V(z)+\gamma V'(z)(\hat z \times \vec{\mathbf p})\cdot \vec{\sigma}## There is translational symmetry in the x-y plane. ##\vec{\mathbf{p}}## is the two dimensional momentum in the x,y...

Homework Statement Figure shows a 50 Hz, high-voltage, transmission line. The relationships between the sending and receiving end voltages and currents are given by the complex ABCD equations: where 'S' stands for sending-end and 'R' stands for receiving-end (a) Given the parameter values...

Homework Statement (a) State what is meant by a ‘distortionless’ and a ‘lossless’ transmission line.(b) A transmission line has the primary coefficients as given below. Determine the line’s secondary coefficients Zo, α and β at a frequency of 1 GHz. R = 2 Ω/m L = 8 nH/m G=0.5 mS/m C=0.23...

I have an expression ##\mathcal{Im}[RT^*e^{-2ip}]=|T|^2\sin p ##, where ##R=Ae^{ip}+Be^{-ip} ## and ##p ## is a real number. This ultimately should lead to ##\mathcal{Im}[A+B+Te^{2ip}]=0 ## upto a sign (perhaps if I didn't do a mistake). There is a condition on ##R ## that it is real...

When sound hits a wall,part of it gets reflected and part of it gets transmitted due to acoustic impedance difference between solid and air. My problem,and point of this question is that having material or gas impedance number is completely useless unless we know the frequency and wall...

In an experiment involving electron scattering from a finite rectangular well of depth 4 eV, it is found that electrons of energy 5 eV are completely transmitted. What must be the width of the well? At what next higher energy can one expect to again observe T = 1? My Attempt: I used the...

Hi, In transmission coefficient T= exp(-2sqrt(2m(U-E)/hbar^2)L), L, as I interpret it, is the distance of the potential barrier. I am wondering if I have N particles all with kinetic energy E, approaching the barrier, can I integrate the transmission coefficient over a distance from infinity to...

I've attached the equation for the transmission coefficient of a particle going through a potential barrier and E < V. I was simply wondering in the limit V --> E, why does T --> 0 (i.e. the V-E term --> 0 and thus the denominator would approach infinity, making T --> 0)? Shouldn't it be...

I have a question about complex reflection and transmission coefficients. For example, I am modeling a wave in air (medium 1) ## \varepsilon = \varepsilon_0 ## reflecting on, and transmitted to, a medium 2 with ## \varepsilon = \varepsilon' -j \varepsilon'' ## If the wave would have traveled...

Hi, The reflection coefficient (R) of an EM wave is, as far as I know, 1 if there is total reflection and -1 if there is total reflection AND the phase changes by 180º. However, we also know that the transmission coefficient is given by T = R + 1 (or by its own formula, which should give the...

Homework Statement Consider an uni-dimensional scattering by a delta function at the origin, given by the potential ##V(x) = g \delta(x)##, with ##g>0##. Using the following result, with ##G(x)## being the green function: $$\Psi (x) = e^{ikx} + g...

Homework Statement Picture of Problem: Homework Equations $$\psi(x) = A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 The Attempt at a Solution I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier...

Homework Statement Two conductors are separated by an insulator. Model the insulator as a square barrier of height 0.01 keV and a width of 5nm. Determine the transmission coefficients for electrons of 7,000 meV. The only thing is I have to use the approximation formula for finding the...

I have an example problem in my book. I have uploaded an image. The part I can't figure out is how to do the last part of the problem to come up with the transmission coefficient. The book gives me a formula but when I plug in all the numbers from the formula into my calculator I get a...

This question relates to rate constants of transition events. The transmission coefficient κ reduces the value of the rate constant compared to the transition state theory (TST) value. I understand κ to be defined as the probability that a reaction coordinate q will proceed to product given that...

Homework Statement A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations The following equation for the transmission coefficient, T, is given: T = [1 + \frac{V_0 ^2...

Hi I have a question on the transmission coefficient in classical optics. When we say that a medium has a transmittance of e.g. 99%, then 99% of the incident light intensity is transmitted. But will the light also acquire a phase? I tried searching the web, but all I found was this...

I have been trying to calculate the transmission coefficient for a quantum tunelling case, but I seem to get the coefficient value more than 1. How is that possible? The equation i used is based on the wikipedia page (I am unable to link because I am underpost). Also typically what are...

V(x) = |g| (δ(x+L)+δ(x-L) Consider scattering from a repulsive twin-delta function potential. Calculate R and T. I'm mostly confused about computing the T coefficients for multiple barriers. Would I compute the T coefficient for the barrier at x = -L and at x = L seperately? Then...

I seem to be getting some arbitrary values from my Scilab code for a function. I have to generate a graph showing the dependence of the transmission on the air gap separating two higher refractive index materials i.e. I want to plot "T" as a function of "d". T = \frac{1}{1 + \beta \sinh^2...

Homework Statement A particle of mass m, (nonrelativistic) energy E, spin 1/2 and magnetic moment \mu*\sigma is traveling in the positive x-direction from large negative x. For x > 0, there is a constant magnetic field B in the positive z-direction. There is no field for x < 0. a) Find...

Hello. I have a question, mathematical in nature. Considering a potential step of height V0 and width a, the amplitude coefficient is t=\frac{2k_1k_2e^{-ik_1a}}{2k_1k_2\cos{k_2a}-i(k_1^2+k_2^2)\sin(k_2a)} Now the transmission coefficient is T=|t|^2 So I need to find the absolute value of...

Homework Statement I have this equation: T=(1+\frac{U_{0}^{2}}{4E(U_{0}-E)}sinh^{2}(2 \alpha L))^{-1} Where α is given by: \alpha = \sqrt{ \frac{2m(U_{0}-E)}{\hbar^{2}}} I have to show that in the limit αL>>1 my equation is approximately given by...

An electron having total energy E=4.46 eV approaches a rectangular energy barrier with U=5.02 eV and L=949 pm. Calculate this probability, which is the transmission coefficient. I thought this would be an easy one, given that T=e-2GL and G=\sqrt{\frac{2m(U-E)}{H}} where H is the...

Homework Statement Find the transmission coefficient for the potential V(x)=-\alpha\left[\delta\left(x+a\right)+\delta\left(x-a\right)\right], where alpha and a are positive constants. Homework Equations T \equiv \frac{\left|F\right|^{2}}{\left|A\right|^{2}} The Attempt at a Solution...

Homework Statement What is transmission probability (T), when the incident particle energy (E) is equal to the energy of the barrier (U)? Homework Equations Equations to transmission and reflection probabilities. http://i950.photobucket.com/albums/ad348/gs5720/img099.png?t=1278212132...

If you have a rectangular square potential barrier of some height, say \lambda/L, and thickness L, what is the transmission coefficient and what is its value in the limit that L goes to 0? Thus you have the height of the barrier going to infinity, while the width goes to zero... Assuming...

Homework Statement E>V_1 & V_2 So it's a step potential wave, setup. Let's set it up along the x axis. At x=0, there is the first step where it is V_1. At x=a, there is another step, where V_2>V_1. Show that the transmission coefficient is...

Work out, with full details, the transmission coefficient for the finite square barrier given by: T = 1/{1+[(V_o ^2)/4E(V_o - E)]sinh^2 (k_2 a)} where T is the transimission probability

If an ensemble of quantum partcles, with energy E, traveling in x direction encounter a very wide potential barrier V0 > E, the ensemble wavefunction will exponentially decay within the barrier. I thought that meant that there was a small probability of detecting an electron within the...

I tried to work out the transmission coefficient and the reflection coefficient for a case similar to the one referred by this website: http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/models/barrier/barsola.htm but instead this time, I reverse the situation and now, that particle...