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1. ### Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation

Yes. Thank you.
2. ### Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation

I am guessing time-energy uncertainty relation is the way to solve this. I solved the Schrodinger equation for both the regions and used to continuity at ##x=-a, 0,a## and got ##\psi(-a<x<0) = A\sin(\kappa(x+a))## and ##\psi(0<x<a) = -A\sin(\kappa(x-a))## where ##\kappa^2 = 2mE/\hbar^2##...
3. ### Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

I do not understand how to use this fact actually. I am trying to eyeball some eigenfunction for ##e^{i\frac{d}{dx}}## but no success as of yet.
4. ### Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

Okay. So I should simply state that the eigenfunctions are all those functions ##f(\phi)## which satisfy ##\operatorname{Ci}\left(\sin^{-1}\lambda f\right)/\lambda +C =\phi## and the corresponding eigenvalue is ##\lambda##. Is that right?
5. ### Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

Thanks for your response. This is what I did $$\frac{df}{d\phi} = \sin^{-1}(\lambda f)$$ On integrating the ##df## integral using online integral calculator $$\frac{\operatorname{Ci}\left(\arcsin\left(\lambda f\right)\right)}{\lambda} = \phi+C$$ It seems this cannot be expressed in terms of...
6. ### Find the eigenfunction and eigenvalues of ##\sin\frac{d}{d\phi}##

Here is what I tried. Suppose ##f(\phi)## and ##\lambda## is the eigenfunction and eigenvalue of the given operator. That is, $$\sin\frac{d f}{d\phi} = \lambda f$$ Differentiating once, $$f'' \cos f' = \lambda f' = f'' \sqrt{1-\sin^2f'}$$ $$f''\sqrt{1-\lambda^2 f^2} = \lambda f'$$ I have no...
7. ### Computing Errors when Data Sets are Given

Yes. Thanks a lot
8. ### Computing Errors when Data Sets are Given

Okay. Thanks a lot. One last question: We used an analog pressure gauge. So is the error in ##\Delta p=## least count of pressure gauge? Or should I take no error in ##\Delta p##? For my post #3 I assumed no error
9. ### Computing Errors when Data Sets are Given

The readings were taken by reducing the pressure by regular intervals of 10 torr and counting the number of fringes that moved outwards within that interval. I have already plotted the graph of ##m## vs. ##\Delta p## and can reasonably say my error in counting ##m## should be ##\pm 1##. I...
10. ### Computing Errors when Data Sets are Given

This is for the lab report I have to submit. ##n## is the refractive index. ##L## is the length of a gas chamber and ##m## is the number of fringes passed as the pressure in the gas chamber changes by ##\Delta p##. We are already given the error in ##L##. I performed the experiment and obtained...
11. ### Understanding Proper Time better

I understand your point. But I am trying to teach myself GR and this exercise is in the first chapter of Carroll. He hasn't introduced curvature and stuff yet. Actually, I got the answer. It is ##\Delta \tau_B = \displaystyle\frac{L}{\gamma v}##. The mistake is in writing the coordinates and is...
12. ### Understanding Proper Time better

Let us denote the events in spacetime before the trip has started by subscript 1 and those after the trip is over by subscript 2. So before the trip has begun, the coordinates in spacetime for A and B are ##A = (t_{A_1},x,y,z)## and ##B = (t_{B_1},x,y,z) = (t_{A_1},x,y,z)##. After the trip is...
13. ### On the Validity of Swapping Dummy Indices in Tensor Manipulation

Oh right! Thanks a lot!