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1 vote

Proper time of two particles being the same when they are under a tree-level interaction

If you want it to be the same then you can set it to be the same. The proper time $\tau$ does not have any particular physical significance. What is important is $d\tau$. So you can set $\tau$ how you ...
Dale's user avatar
  • 102k
2 votes

After how many bounces will a ball's mechanical energy equal zero?

First approximation: ball and surface are perfectly rigid. This implies the collision is instantaneous, and therefore elastic. The bounce height is always the same. Second approximation: ball and ...
Alex I's user avatar
  • 406
0 votes

Generalized momentum

The total momentum $P=\sum \partial L/\partial x_i$ in flat Euclidean space in Cartesian coordinates is conserved, if the Lagrangian $L=T-V(x_1,x_2,\dots x_n)=T-V'(R,x_1-x_2,\dots ),$ rewritten in ...
Roland F's user avatar
2 votes

Generalized momentum

Generalized momentum $p^i$ is conserved if the Lagrangian function $\mathscr{L}$ doesn't depend on the generalized coordinate $q^i$. It's readily proved from the Lagrange equation, $$\frac{d}{dt} \...
basics's user avatar
  • 9,802
12 votes

After how many bounces will a ball's mechanical energy equal zero?

Never, if you treat the problem with the laws of classical mechanics, treat both the ball and the ground as "macroscopically" rigid, and you don't set a threshold $\overline{h}$ under which ...
basics's user avatar
  • 9,802
0 votes
Accepted

Problem when deriving formula of the momentum of photons in photoelectric emission

The relations $KE=\frac{1}{2}mv^2$ and $p=mv$ hold for massive non-relativistic (that is, $v\ll c$) particles. They cannot be used for photons, as photons are massless and travel at a speed of $c$. ...
Sturrum's user avatar
  • 459
0 votes

Problem when deriving formula of the momentum of photons in photoelectric emission

The energy of a photon is $E = pc$, without the factor $\frac{1}{2}$.
Jesse's user avatar
  • 71
0 votes

Fallacious derivation of the rocket equation

This must be equal (and opposite) to the impulse imparted on the rocket during that time and hence the rate of change of momentum. $$ -\dot{m}v_e = \frac{d}{dt} (mv) = \dot{m}v + m\dot{v} $$ This is ...
Ján Lalinský's user avatar
3 votes

Is it theoretically possible to aim a neutrino's trajectory without using a massive celestal body to aim it?

Neutrinos interact so seldom that it is not possible to align them after they are created. The DUNE experiment at FermiLab does create a beam of neutrinos. They actually create a beam of protons. Then ...
mmesser314's user avatar
0 votes

Conflicts between Bernoulli's Equation and Momentum Conservation?

Momentum equation is force relation for same area 1D situation. For compressible flow, $v^2/2$ is used in the energy balance relations. The key point is that this equation is never used for actual ...
HeonSeok Lee's user avatar
2 votes

Momentum distribution of nucleons inside the deuteron (Paris potential)

You forgot the Argonne V-18 potential: https://www.phy.anl.gov/theory/research/momenta/
JEB's user avatar
  • 34.9k
0 votes

Energy and momentum operators using Hamilton's equations

There's a conceptual mistake there. What follows could find an answer with the relationship between Poisson brackets in classical mechanics and the commutator in quantum mechanics. The conceptual ...
basics's user avatar
  • 9,802
1 vote

Energy and momentum operators using Hamilton's equations

As it stands, the question is meaningless since Eq.(1) is not the definition of an operator in the Hilbert space as, instead, Eq.(2) is. The point is that $t$ labels different states in the Hilbert ...
Valter Moretti's user avatar
1 vote
Accepted

Total momentum of a fluid in a pipe

A cylindrical shell with small thickness $dr$ at a distance $r$ from the centre of the pipe has volume $dV = 2 \pi L r \space dr$ and so contains a mass $dm = \rho dV = 2 \pi \rho L r \space dr$ of ...
gandalf61's user avatar
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2 votes

Total momentum of a fluid in a pipe

You need to evaluate the integral defining the momentum, $$ \mathbf{Q} := \int_V \rho \mathbf{u} $$ performed over the volume of fluid $V$ of your interest. Here $\rho$ and $\mathbf{u}$ are the ...
basics's user avatar
  • 9,802
0 votes

Weinberg QFT problem 2.1: transformation of quantum states

Note that $\Lambda$, $L(p)$ and $L(\Lambda(p)$ are all pure boosts in y-z plane so that any three vector along x-axis is unaffected by $W(\Lambda,p)=L^{-1}(\Lambda p)\Lambda L(p)$. Thus $W(\Lambda,p)$...
Damo's user avatar
  • 31
0 votes

Definition of expectation value for momentum

For any function $F(\vec r)$ of position $\vec r$, the expectation value is defined as: $$ \langle F\rangle = \int d^3r F(\vec r) P(\vec r)\;,\tag{1} $$ where $P(\vec r)$ is the probability density in ...
hft's user avatar
  • 21.1k
4 votes

Definition of expectation value for momentum

In the $x$-representation, the expectation value of the momentum operator $P$ in a (pure) state $|\psi\rangle$ described by the (position space) wave function $\psi(x)=\langle x|\psi\rangle$ is ...
Hyperon's user avatar
  • 6,596
4 votes

Where did the rotational energy come from?

Work is force times distance. If the force is applied off-center then the distance over which the force is applied will be larger. So, the additional energy is given by additional work done by the ...
Dale's user avatar
  • 102k
2 votes

How to understand $W=pc$ in Feynman's Lectures on physics?

$$W=\sqrt{p^2c^2+m^2c^4}$$ approaches $W=pc$ for $p\gg mc$ and $W=mc^2+{p^2\over 2m} = mc^2+{1\over 2}mv^2$ for $p\ll mc$.
my2cts's user avatar
  • 24.9k
2 votes
Accepted

How to understand $W=pc$ in Feynman's Lectures on physics?

$pc$ is the total energy of a massless relativistic particle, like the photon. Electrons do have mass, so what's the catch? Well, if the momentum of the electron is very big, then we can neglect the ...
Gabriel Ybarra Marcaida's user avatar
2 votes

Difference of $p^0$ and $E_p$

I see such an expression: $$ \frac{1}{2E_p}e^{-iE_p(x^0-y^0)}=-\frac{1}{2\pi i}\int_Cdp^0\frac{e^{-ip^0(x^0-y^0)}}{(p^0-E_p)(p^0+E_p)} $$ I know that this equation can be derived using Cauchy's ...
hft's user avatar
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