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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Where does the partial derivative come from in Sakurai's derivation of the momentum operator?

How is the momentum operator derived in Dirac formalism? I am reading Quantum Mechanics by Sakurai and he gives the following derivation. But I don't understand how he goes from the third equation to ...
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731 views

What is the most general expression for the coordinate representation of momentum operator?

I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$. One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th ...
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4answers
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Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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808 views

The Momentum Operator in QM

I've seen the 'derivation' as to why momentum is an operator, but I still don't buy it. Momentum has always been just a product $m{\bf v}$. Why should it now be an operator. Why can't we just multiply ...
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Walter Lewin Lecture 16 - Ball bouncing on wall?

I never did Physics in university and I consider that a mistake so I am correcting that now by teaching myself. To that extent I have been watching the MIT lecture videos by Walter Lewin and I am ...
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423 views

Does constraint for speed of Electric and magnetic fields violates Conservation of momentum or Newton's third law?

I'm just a beginner so bear with me. Consider two frames at rest wrt to each other separated by distance enough for light to take a minute or so. At a given instant we create two large dipoles by some ...
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2answers
2k views

Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
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3answers
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Why is momentum conserved in an inelastic collision and kinetic energy is not conserved? [duplicate]

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
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2answers
853 views

Does a force really act on a body during a collision?

Consider two bodies A(black) and B(red) having equal mass. A is moving at a constant speed towards B, which is stationary. At certain point of time, they collide elastically, $\therefore u_{A}=v_{B}$ ...
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1answer
139 views

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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2answers
2k views

Pair production - mathematically?

Allover the web i am only seeing a statement similar to this: Pair production is not possible in vaccum, 3rd particle is needed so that conservation of momentum holds. Well noone out of many ...
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116 views

4-Momentum conservation for particle annihilation

Disclaimer: this is a homework question, so I am happy with just a hint or the expressions needed to proceed with my understanding. I am working on the momentum conservation of a ...
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4answers
14k views

How does the 'water jet pack' work?

So I was cruising around at YouTube and saw this sweet video, and as I was watching started to wonder: "How is this possible?". For a little bit of background, in case you decide to not watch the ...
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1answer
336 views

Water bottle rocket: Where does the energy go without water?

In Portland's OMSI there is a hands-on water bottle rocket station. (https://www.youtube.com/watch?v=cdtmVY76_PQ). The rockets are normal PET bottlers. The visitors fill their bottle with an amount of ...
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3answers
599 views

Expectation of momentum in the bound state

Is it logically correct to assert that the expectation of the momentum $$\langle \hat p \rangle=0$$ for any bound state because it is bound to some finite region? What is the physical interpretation ...
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2answers
793 views

Origin of motion and relative speed of bodies in the universe

Charged particles can hit the earth at relativistic speeds. But it seems that all large bodies have fairly low relative speed. Of course, speed can increase considerably when a body orbits close to a ...
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3answers
2k views

Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
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4answers
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Is it possible to lift yourself off from the ground?

Say for instance a person who was strong enough to lift double his body weight. If he placed his hands under his bottom and tried to lift$^1$ himself$^2$ off the ground, could he? -- $^1$In a ...
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0answers
207 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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2answers
1k views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
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1answer
555 views

How to get the new direction of 2 disks colliding?

I'm developing a 2D game including collisions between many disks. I would like to know how I can get the angle corresponding to the new direction of each disk. For every disk I have this information ...
2
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1answer
460 views

Rocket drive and conservation of momentum

I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive. Let $v$ be the velocity of the ...
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3answers
836 views

Train crash: are these situations alike? [duplicate]

I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the ...
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2answers
550 views

How does a rocket's exhaust gas' momentum propel a rocket?

During the launch of a rocket into space, the exhaust gases from the engine possess momentum. Outline, with the help of an equation, how this causes the rocket to be propelled upwards. Can ...
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2answers
229 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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349 views

Ball flying towards me - Newton's third law is violated?

I was trying to answer the question of the flying ball here on the basis of Newton's third law and momentum conservation. Here is what I have tried. Lets take a ball mass of $m_1$ (index 1 is the ...
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1k views

Elastic Collision And Momentum

The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = ...
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4answers
268 views

Which is the right explanation for rocket motion? [duplicate]

What actually causes a rocket to move? Is it the pressure in the rocket engine or the amount and velocity of mass that is being ejected out. The reason I am asking is, I found these two explanations ...
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4answers
851 views

Where does the energy required to stop a moving body come from and go?

For a long time, I have been thinking about this: In order to stop a moving body, I have to apply impulse to change the existing momentum to $0$. For the impulse I have to impart force on the moving ...
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2answers
158 views

Determine $p_x$ from $[x,p_x]=i\hbar $ [closed]

With $[x,p_x]=i\hbar $, how to determine the form of the operator $p_x$?
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6answers
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Can a Skydiver Land On a Large Slide and Survive?

Please forgive my lack of artistic ability, but here's my question: Consider that a skydiver, without using his parachute, were to fall exactly parallel to a giant curved slide that starts at ...
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2answers
230 views

What canonical momenta are the “right” ones?

I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the ...
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421 views

How multiple objects in contact are resolved in an inelastic collision, when edge normals don't “line up”

In a case I understand, let's say I have an object A moving at velocity V toward 3 objects in contact B, C, and D: The momentum of A is the mass of A times its velocity. To figure out how the ...
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766 views

Best current bounds on nonconservation of momentum?

It's not straightforward to test conservation of momentum experimentally, and many experiments that seem like tests really aren't. For example, in a Newtonian system of identical particles that ...
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7answers
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Ball flying towards me or me flying towards ball

Suppose a ball is flying towards me at a speed of 10m/s and that, on impact, I feel "x" amount of pain. If, instead, it was me flying towards the ball at the same speed, with all other conditions ...
8
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2answers
581 views

Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
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2answers
287 views

Is it possible to determine the outcome of any impact knowing only the ratio of masses? [duplicate]

In elastic collisions in 2-D if two balls $A$, $B$ ($m_A = m_B$, $R = 1$) have equal mass we can determine in advance the outcome of the collision. If cue-ball $A$ impacts object-ball $B$ (at rest) ...
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3answers
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The elusive difference between impulse and momentum

1) In classical mechanics, impulse is the product of a force, F, and the time, t, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ...
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4answers
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Uncertainty Principle for a Totally Localized Particle

If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
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136 views

Schrödinger equation in momentum space

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose. It then ...
3
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2answers
116 views

What happens when two bodies collide in a dynamics point of view?

I'm a high school student learning about energy and momentum. What confuses me is the things with elastic and inelastic collisions. I completely (in my opinion) understand those concepts in energy ...
3
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1answer
368 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
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2answers
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What is the Momentum Operator?

I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return ...
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2answers
368 views

What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
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1k views

Energy is actually the momentum in the direction of time?

By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong?
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4answers
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Can a particle have momentum without energy?

Can a particle have linear momentum if the total energy of the particle is zero? Even if a particle has a certain velocity, can its potential energy cancel out the kinetic energy as to add to zero ?
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Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the de Broglie relation $p=\frac{h}{\lambda}$ comes from? I know that for light (which has no rest mass), the following is true: $E=pc$ and $E=hf$ so, $$pc=hf \Rightarrow ...
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327 views

Why Can a Skydiver Hit the Ground and Be Killed? [duplicate]

This is a follow on question from Physics SE Question "Can a Skydiver Land On a Large Slide and Survive?". User Steeven gives this answer here. User Dargscisyhp asks: What is it exactly that ...
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0answers
83 views

Is there a general formula to translate from *canonical* to *physical* momentum?

In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: ...
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2answers
715 views

Why the photon can't produce electron and positron in space or in vacuum?

$$\frac{hc}{\lambda} = K_e + K_p + 2m_e c^2$$ could be the energy conservation equation for a photon of wavelength $\lambda$ decaying into a electron and positron with kinetic energies $K_e$ and $K_p$ ...