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##...
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?
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...
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...
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
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...
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...
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...
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...
Property (a) simply states that a second rank tensor that vanishes in one frame vanishes in all frames related by rotations.
I am supposed to prove: ##T_{i_1 i_2} - T_{i_2 i_1} = 0 \implies T_{i_1 i_2}' - T_{i_2 i_1}' = 0##
Here's my solution. Consider,
$$T_{i_1 i_2}' - T_{i_2 i_1}' = r_{i_1...
The given lagrangian doesn't seem to correspond to any of the basic systems (like simple/ coupled harmonic oscillators, etc). So I calculated the momentum ##p## which is the partial derivative of ##L## with respect to generalized velocity ##\dot{q}##. Doing so I obtain
$$p =...