Thank you both for the suggestion. So I have ##\Phi^*(p_x,0)\Phi(p_x,0)=\frac{1}{2\pi \hbar} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{i(\frac{p_xy}{\hbar}-\frac{p_xx}{\hbar})}\Psi(x,0)\Psi^*(y,0)\mathrm{d}y \mathrm{d}x##, and so ##\int_{-\infty}^{\infty}...
Homework Statement
Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi} \int_{-\infty}^{\infty}e^{i(k-k')x} \mathrm{d}x$$
Show that if a position space wave function $$\Psi(x,t)$$ is normalized at time t=0, then it is also true that the corresponding...
Homework Statement
In deriving the expression ##\frac{f'-f}{f}=\frac{gH}{c^2}=\frac{GM_s}{R_sc^2}## , it was assumed that ##\triangle f=f'-f## was small, and that the photon had a constant mass of ##\frac{hf}{c^2}##. Suppose that a star is so dense that ##\triangle f## is not small.
(a) Show...
Oops, I always make that mistake. I've come across something puzzling in (c) when finding the kinetic energy of particle R, ##K_R##. I know ##E_R=K_R+m_Rc^2##, so ##K_R=E_R-m_Rc^2=0##, since ##E_R=m_Rc^2##. But from L's perspective, particle R is certainly moving, so how can its kinetic energy...
Thanks for your reply. My prof feels the same way as you, and my textbook says as much; "we feel that relativistic mass does not lead to any deeper physical understanding, so we will not treat it in this text". So it's weird / frustrating to see a question about it.
For (c), in computing the...
Homework Statement
Two relativistic particles "L" and "R", each of rest mass ##m_0##, are moving at speed ##v## towards each other (in the frame of an observer). They collide squarely and are stationary afterwards.
(a) From the perspective of one particle, what is the oncoming speed of the...
Interesting - we've covered the Lorentz transformation, but not four-vectors. My class gives a brief overview of SR, but maybe I'll see it in future.
I have another question that I'm editing into the OP now - It's somewhat related, but I didn't want to flood the section with threads.
EDIT...
Thanks very much for the help. It worked like a charm - the last part of the derivation that I ended up using was pretty neat. My only worry is that my prof will wonder how I thought to express ##E'## and ##cp'## in that way.
Homework Statement
[/B]
A particle of mass m is moving in the +x-direction with speed u and has momentum p and energy E in the frame S.
(a) If S' is moving at speed v, find the momentum p' and energy E' in the S' frame.
(b) Note that E' \neq E and p' \neq p, but show that...
Homework Statement
A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of θ_0 with respect to the x'-axis.
(a) Show that the length of the rod as measured by a stationary observer is given by
L=L_0\sqrt{1-\frac{v^2}{c^2}cos^2θ_0}
(b)...
Thanks, I'm not sure how I didn't see it, but just this little prompt helped me with the algebraic manipulation. In case anyone needs help with this sort of problem in the future:m=(|\vec{T}|cosθ)/g
\vec{a}=(-g|\vec{T}|sinθ)/(|\vec{T}|cosθ)
\vec{a}=(-gsinθ)/(cosθ)
Homework Statement
On her flight home at Thanksgiving, Margaret decides to apply the physics she has learned in PHYC1300 to measure the speed of the aircraft when it takes off. She dangles her watch from a string while the aircraft accelerates down the runway. Draw a free body diagram of the...
Thanks to both of you. I don't know how I managed to miss that while reviewing my notes.
I also seem to have done the x component wrong. The initial x position was 12.4m, not 0m, which gave me the correct answer with the pythagorean theorem. Thanks again.
Now if I want the initial velocity of...
Homework Statement
So it's a projectile motion problem. I draw a graph showing the parabolic trajectory of the ball, with the start point at the origin. It's final x = 24.8m and final y = 0m
Homework Equations
We have three constant acceleration equations we use in my course:
\vec{v}_{fx}...