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    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.
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    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##
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    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(...
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    I Divergence Theorem not equaling 0

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

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

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

    Is v(r) ≡ v(x,y,z)
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    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?
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    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
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    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))
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    Maximum Kinetic Energy from a Physical Pendulum

    Would I have to use cos (x) instead of sin (x)? Umm yes thats the question :)
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    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?
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    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 +...
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    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?
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    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
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    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...
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    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...
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    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...
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    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?
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    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
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    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
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    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...
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