The (5,15) and the -9s refer to the coordinates of the points that make up the parallelogram. The first coordinate, 5, is the x-coordinate of one corner of the parallelogram and the 15 is the y-coordinate. The -9s refer to the x-coordinates of the other three corners of the parallelogram.
Yes, you are correct in assuming that the expectation value of ##r^2## is equivalent to finding it for ##x^2+y^2##. The first three Landau levels are given by ##\psi_{(n=0)(l=0,1,2)}##.
In order to obtain the relativistic lower order correction of the Coulombian potential, one needs to use the scattering amplitudes and calculate the corrections due to the higher order terms that appear in the interaction due to relativistic effects. This can be done by computing the Feynman...
The equation that you have obtained is correct. To show that the line element can be written in the form ##\mathrm{d}s^2=-A(r,t)\mathrm{d}t^2+B(r,t)\mathrm{d}r^2+r^2(\mathrm{d}\theta^2+\sin^2{\theta}\mathrm{d}\phi^2)##, you need to make use of the fact that the transformation ##t'=f(r,t)## is a...
?Thank you. A:The phase of the reflection and transmission coefficients is not important for Snell's law of refraction. The only thing of importance is the ratio of the sines of the incident and refractive angles. The phase is essentially a constant, and does not affect the value of the ratio.
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It looks like you are not correctly modifying the signal with the cosine theta vector. The theta vector should be used to modify the phase of the signal, not its amplitude. Try modifying the signal with a phase shift equal to mu * (cos(theta) - 1) * t1 and see if you get the desired results.
There are a couple of things you can try to reduce the overshoot in your PID controller design. First, you can try increasing the proportional gain (Kp) or decreasing the integral gain (Ki). Increasing Kp will increase the speed of response, which can reduce the overshoot, while decreasing Ki...
\frac{N}{N_0}=\frac{V}{V_0}Proof:Let N be the average number of particles, N0 be the total number of particles, V be the total volume and V0 be the volume of a given space.By definition, we know that N is equal to the total number of particles divided by the total volume. Thus, N = N0/V...
Unfortunately, MATLAB alone is not sufficient to solve this problem. You will need to use an additional software package such as STK (Systems Tool Kit), which is a simulation software suite developed by Analytical Graphics Inc that is used to model space missions. STK can be used to calculate...
Any help is appreciated.The answer to your question lies in the equation you derived:$$e^{i(\alpha_1 - \alpha_2)} = \frac{V_{21}}{|V_{12}|}$$This equation tells us that the difference between the phases is equal to the ratio of $V_{21}$ to $|V_{12}|$. Now, if we know one of these phases, we can...
A:The energy-momentum tensor for the interacting part of the Lagrangian is defined by$$T^{\mu\nu}_{\text{int}} = \frac{2}{\sqrt{-g}} \frac{\delta(\sqrt{-g}\mathcal{L}_{\text{int}})}{\delta g_{\mu\nu}}$$Hence,\begin{align}T^{\mu\nu}_{\text{int}} &= \frac{2}{\sqrt{-g}} \frac{\delta(\sqrt{-g}A_\mu...