In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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How to get the accurate relativistic momentum form for photons? [duplicate]

I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I ...
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79 views

Inner product of position and momentum eigenkets

Let's define $\hat{q},\ \hat{p}$ the positon and momentum quantum operators, $\hat{a}$ the annihilation operator and $\hat{a}_1,\ \hat{a}_2$ with its real and imaginary part, such that $$ \hat{a} = ...
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Losing mass in space

So I came across a question while studying laws of motion. Roughly, this is how it goes: There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage ...
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Spacecraft momentum question [closed]

Assume you're sitting in your spacecraft. The mass of you and the spacecraft is 2000 kg. You're traveling at 200km/h through the vacuum of space. You have a thruster pointing in the direction you're ...
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34 views

Spacetime and the conservation laws

I'm reading Peter Atkins' book, Galileo's Finger, and in the chapter on energy, he makes the points that the conservation of momentum stems from the shape of space (that it's smooth and not lumpy) and ...
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61 views

Does mass equal angular momentum?

At the wikipedia pages for angular momentum ($L$) and moment of inertia ($I$) we find the equations: $$L=I \omega$$ $$I=m r^2$$ where $m$ is mass and $r$ is the distance between said mass and ...
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question about derivative of momentum = force proof***

I was trying to prove it 2 ways, 1st way: $$p=mΔV$$ $$a=ΔV/t$$ $$ΔV=at$$ $$p=m*a*t$$ Remember $$F=ma$$ $$F(t)=p$$ The derivative of momentum just gives us the "regular force" since b4 that momentum ...
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Difference between momentum calculated from wavefunction and momentum computed by energy formula

Take a quantum well, for example. The energy of an electron is given by: $E_n=k_n n^2$. Moreover, we know that the momentum of an electron with energy $E_n$ is given by: $p=mv=m(2T/m)^{1/2}$, where ...
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1answer
68 views

Simultaneous conservation of linear and angular momentum

Suppose there is a ring in the space where there is no gravity. The width of the ring is $r$ which is negligible compared to its inner radius $R$. The ring is in horizontal position. Now imagine a ...
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3answers
79 views

Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in ...
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0answers
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Calculating a spacecraft's deflection angle [closed]

There is a spacecraft with mass $M_1$ moving in a certain trajectory with a constant speed $V_r$. To modify its trajectory, a engine is turned on and starts ejecting gas at a speed $V_g$, which is ...
2
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1answer
76 views

Does the average momentum vanish for an eigenstate of the simple harmonic oscillator?

Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$. $\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can ...
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2answers
144 views

Photons have no mass. So, why does $E = pc$ hold? [duplicate]

It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The ...
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1answer
46 views

What's wrong with this simple derivation of energy flux in a photon gas?

In a photon gas, we know that pressure, $P$, and energy density, $u$, are related by: $$P=\frac{u}{3}$$ We also know from relativity that the momentum of a photon is $$p=\frac{E}{c}$$ Finally, the ...
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62 views

Understanding Momentum

I'm trying to learn more about momentum and I'm a little confused. Based on my understanding, in an isolated system, total momentum is conserved in a collision. Today in class the professor went over ...
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1answer
47 views

calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
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4answers
153 views

Definition of force, kinetic energy and momentum

I've edited the post. Q1 and Q4 are the important ones but I didn't delete Q2 and Q3 since some older answers would not make sense anymore. To begin with, the formula of the kinetic energy $T$ is ...
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1answer
24 views

How would one compute the angle of deflection, in a relativistic collision - underspecified system?

Consider the simplistic case of two identical mass particles colliding elastically with the second particle initially stationary and the first particle travelling with energy $E$. By conservation of ...
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1answer
57 views

Momentum of Light Question [duplicate]

Since light beams carry momentum, why would a person holding a flashlight not feel a recoil similar to that of a rifle being fired?
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Force as change in momentum vs. change in velocity

Is there ever a situation where the distinction between $F = m \frac{dv}{dt}$ and $F = \frac{dp}{dt}$ is important? I can't think of a situation where one is true and not the other (assuming only ...
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1answer
40 views

changes in horizontal velocity and the effect on time airborne (thus overcoming gravity)

I would like to know if a object is launched horizontally in the air at a lower speed and a higher speed, why does the higher speed keep it airborne longer. what are the forces and why does gravity ...
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Can acceleration be achieved without reaction mass?

In a previous question, I asked whether a flashlight can accelerate me. The answer is yes. This has led me to wonder, this is inferior to all other known propulsion methods in all aspects except one: ...
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Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
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1answer
81 views

Quantum Mechanics - Finding momentum probability density [closed]

everyone. I got a bit stuck on 2(iii), this is supposed to be a easy question, but i don't know how you get the square term? I thought you just do the Fourier transform, but then I got some ...
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Why not shoot a marble sized spacecraft at the moon?

I was thinking about the Google XPrize for Space Travel the other day. In order to claim the prize of building a robot that goes to the moon, travels 500m, and relays data, I had the idea of building ...
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How does $p_x$ commute with $p_y$, i.e. $[p_x,p_y]=0$? [closed]

I know it's a simple and basic question but would someone show me how to evaluate $[\hat{p}_x,\hat{p}_y]$?
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Why is momentum quantized in a 1D box even though the operator doesn't give eigenstates?

We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?
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263 views

Complex conjugate of momentum operator

Consider momentum operator representation in position space. $$\hat{p}=-i\frac{\partial}{\partial x} \,\ \text{and its eigen functions are } e^{ipx} \,\text{and} \,\ e^{-ipx}.$$ ...
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1answer
39 views

Work done or not in this case?

I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any ...
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1answer
78 views

What happens to the acceleration of a body undergoing constant force?

Here's the problem I have, specifically relating to a rocket in deep space: A rocket burns fuel at a constant rate. Assuming its mass remains constant, what happens to its acceleration? I seem to get ...
3
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1answer
155 views

Interpretation of Conjugate Momentum in Field Theory

The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given ...
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Definition of momentum-entangled particles

When we can say that two particle are momentum entangled ? I just read an article where it's said that two momentum entangled particles share the same momentum value in opposite directions no matter ...
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How we can manipulate the momentum of a particle?

Is there any way to affect a particle's momentum value?
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188 views

Why don't we substitute for $p$ in $E = pc$?

See, the energy of a photon is given out by $E = pc = hv$ why don't we substitute for $p$ in $E ^2= p^2 c^2 + m^2 c^4$ by putting $p = \gamma mv$ and then get a value for $m$ (which will be $0$ for a ...
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1answer
88 views

Why won't this reactionless drive idea work (motor with a moving weight in space)

I know people will say it violates many laws of motion and conservation but could anyone explain why it is so? It's NOT a question about free energy. Imagine a motor in space. It has an arm (rod) ...
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Measurement of Mass and Momentum of a particle simultaneously

In quantum mechanics can the mass and the linear momentum of a particle be measured precisely or do they commute ?
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About photons and mirrors

If a photon hits a 'perfect' mirror (with no environment interference) would the mirror move a bit?
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56 views

What are the general solutions to a hard sphere collision?

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
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What happens with a tunneling particle when its momentum is imaginary in QM?

In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to ...
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Equilibrium that is not stable

Consider a system which is in an equilibrium state. Now, a small perturbation causes it to start oscillating about the equilibrium state, but over time, the momentum with which it overshoots the ...
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1answer
58 views

Recoil from a shotgun

First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this. If I were to sit on an office chair on a laminated ...
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2answers
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Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
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1answer
61 views

Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
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1answer
25 views

Do I need the exact velocity when experimenting with sliding coins?

I'm doing a home experiment but it's not going very well. I'm pushing coins on a table. I'm taking the time for how long it takes coin A to hit coin B and then I divide it by the time between them ...
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19 views

Calculating rate of change of momentum for a package [closed]

A helicopter is flying to the right (in the $+x$ direction) with a constant speed $v$, carrying a package of mass $M$ suspended below it using a cable as shown in the figure. (You can assume that $H$ ...
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4answers
594 views

Deriving $F = ma$ - Newton's Second Law of Motion

Context: In my textbook it is given: 'momentum' short for 'linear momentum': Mass = $m$, momentum is $p=mv$. In time $\Delta t$, momentum changes by $\Delta p$, the rate of change of momentum is: ...
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90 views

In the Dirac equation, do $\alpha$ and $p$ commute?

The Dirac Hamiltonian is given as $H = \vec \alpha·\vec pc + \beta mc^2$ , Do the alpha and beta operators commute with the momentum operator? If yes then how?
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Why $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
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Momentum Operator in Quantum Mechanics

1) What is the difference between these two momentum operators: $\frac{\hbar}{i}\frac{\partial}{\partial x}$ and $-i\hbar\frac{\partial}{\partial x}$? How are these two operators the same? My ...
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133 views

Spring Damper System : Recoil Reduction

I am designing a man-"portable" 30mm sniper rifle. Although it may be classified as a anti-materiel cannon. I have the mass of the round in total, and the mass of the projectile leaving the barrel, ...