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1. Probability wave function is still in ground state after imparting momentum

Thank you. Do you by any chance know any way to solve that integral by hand? I solved it on mathematica and it gave me ##P=e^\frac{-{k_{0}}^{2}\hbar}{4mw}## but I have no idea how to solve it by hand. Thanks again.
2. Probability wave function is still in ground state after imparting momentum

Ah right. So would this be the probability of the system still being in the ground state? ##\left | \int_{-\infty}^{\infty} \psi_{0} \psi_{0} e^{ik_{o}x}dx\right |^2=P##
3. Probability wave function is still in ground state after imparting momentum

Homework Statement An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state. Homework Equations ##\psi _{0} =\left(...
4. I Divergence Theorem not equaling 0

Sorry, I forgot to mention that f(r) = div (grad (1/r))
5. I Divergence Theorem not equaling 0

Why is it possible that ∫∫∫ V f(r) dV ≠ 0 even if f(r) =0
6. Position vector in spherical coordinates

Is the position vector r=xi+yj+zk just r=rerin spherical coordinates?
7. I Vector Fields

Is v(r) ≡ v(x,y,z)
8. Question about the Dirac Delta Function

Homework Statement Find the Fourier spectrum of the following equation Homework Equations ##F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]## The Attempt at a Solution Would the Fourier spectrum just be two spikes at ##+\omega _0## and ##-\omega _0## which go up to infinity?
9. Phasor angular velocity for a triangle wave?

What would the angular velocity for a phasor be for a triangle wave? I think it would vary sinusoidally but I cant find an expression
10. Maximum Kinetic Energy from a Physical Pendulum

Okay, so i drew a picture and realised that I made a mistake. I got to Change in x = l/2 * (1- cos(x))
11. Maximum Kinetic Energy from a Physical Pendulum

Would I have to use cos (x) instead of sin (x)? Umm yes thats the question :)
12. Maximum Kinetic Energy from a Physical Pendulum

I used a factor of sin (x) because the change in the y axis * mg is equal to total potential energy y = r sin (theta) when changing between polar and cartesian coordinates Is this the wrong way to think about it?
13. Maximum Kinetic Energy from a Physical Pendulum

Homework Statement Determine the maximum kinetic energy of a uniform rod of mass 0.5Kg and length 0.75 that has an angular displacement of 5 degrees. Homework Equations y = rsin (x) where x is the angular displacement The Attempt at a Solution Using conservation of energy ETotal = EMech +...

Thank You :)
15. Disintegration Energy of Beta Plus Decay

Ah i think I understand Q = ((mC- 6mE) - (mB - 5mE + mE))c2 Q = (mC - mB - 2me) c2 Is this right?
16. Disintegration Energy of Beta Plus Decay

But that leads me to Q = ((mC+6mE) - (mB + 5mE + mE))c2 Which gives me Q= (mC + mB)c2
17. Disintegration Energy of Beta Plus Decay

Homework Statement The radionuclide 11C decays according to 116C → 115B + e+ + v Show that the disintegration energy is given by Q = (mC - mB - 2me) c2 Homework Equations Q = (mi - mf) c2 The Attempt at a Solution [/B] Q= (mC - mB - me) c2 Im probably missing something obvious but I can't...
18. Relativistic Centre of Momentum Frame

S' frame is moving at a velocity v w.r.t S frame. Let velocity of Particle 1 = U1 in S frame and particle 2 = U2 in S frame therefore Particle 1 = U1' and particle 2 = U2' in S' Frame Since particle 2 is at rest in S frame, its velocity in S' frame is equal to the velocity of the S' frame...
19. Relativistic Centre of Momentum Frame

Homework Statement A partical of mass m ha speed 0.546c relative to inertial frame S. The particle collides with an identical particle at rest in the inertial frame S. Relative to S and in terms of c, what is the speed of S' in which the total momentum of these particles is 0. Homework...
20. Implicit Differentiation z=f(x/y) meaning

So i would let u=x/y so then $$\frac{\partial z}{\partial x} = \frac{\partial z }{\partial u} \frac{\partial u }{\partial x} = \frac{f'}{y}$$ cause I'm guessing $$\frac{\partial z }{\partial u} = f'$$ or am i completely wrong?
21. Implicit Differentiation z=f(x/y) meaning

I'm sorry, I'm just really unsure how to apply the chain rule. So is ∂z/∂t = ∂/∂x(x/y) * F' ? But I'm unsure how to find all the other ones. I have the solutions attached to this post but I have no idea how to get them. Thank You
22. Implicit Differentiation z=f(x/y) meaning

Mod note: Moved from the Homework section 1. Homework Statement This might seem like a stupid question but I'm unsure what z= ƒ(x/y) means? I'm not sure how I would find ∂z/∂x , ∂z/∂y just from this statement either. Thank you Homework Equations The Attempt at a Solution
23. Elastic collision between alpha particle and gold Nuclei

Homework Statement When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 3.94 MeV alpha particle has a head-on elastic collision with a gold nucleus that is initially at rest. What is the kinetic energy of (a) the recoiling nucleus and (b) the rebounding...