Questions tagged [momentum]
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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Does it take more energy to bring a car to a halt if it is still accelerating on impact than travelling at constant speed?
So my physics is quite rusty, been out of varsity for a while.
A friend asked me this and I am still pondering. Here is the scenario:
2 Cars are travelling towards a wall, and make impact with the ...
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What's the Force acting on an object suspended in another object during freefall [closed]
Let's say we drop a box. In that box we have a rope attached from 2 ends onto a load in the center. Now, if we drop the box, what would be the force which acts on the load. What would be the overall ...
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Why isn't the fact that energy is quantized in quantum mechanics inconsistent with Newtonian and relativistic physics? [closed]
In Newtonian mechanics, energy, momentum, and position are all related. Velocity and position are related by $v = \frac{dx}{dt}$, and momentum relies on both via $p = mv$. Motion gives rise to a form ...
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Do chargeable batteries break the third law of newton? [closed]
When you charge a lithium battery for instance the electron momentum that coming out of the source is stored in the battery. The problem is that the direction of the electron might change when ...
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How does changing the mass of a block affect its speed after collision? [closed]
I'm doing a physics IA investigating how mass of a block affects it's velocity after collision when initial momentum is constant. I did this by using a pendulum setup with a constant release angle (...
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There are two balls heading toward each other and have a glancing collision, how would you solve for the velocity of center of mass? [closed]
I tried using the typical equation for the velocity of the center of mass for regular collisions, but it doesn’t seem quite right since the balls are offset from each other. I’m thinking the velocity ...
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Confusion about Deriving Momentum Operator and Hamiltonian Operator
In Sakurai's quantum mechanics, the derivation of momentum operator and Hamlitonian operator is based on spatial translation and time translation as below,
for spatial translation and momentum ...
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Canonical and kinetic momenta vs gauge dependence
I am struggling a bit to understand the concept of gauge invariance/dependence with canonical momentum.
For instance, if we consider a Hamiltonian of a particle in an electromagnetic field described ...
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Are $E_i A_j + E_j A_i$ components of a tensor?
I want to know whether the quantities $E_i A_j + E_j A_i$ are components of a tensor? Here, $E_i$ are the components of the electric field from a particle with charge $q$ (at rest in the frame I am ...
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Question about sign convention in electron-hole crystal momentum
I was trying to understand a toy model Raman scattering diagram from a paper on pressure tuned moire phonons, when I realized the standard electron hole pair creation diagram confuses me. By ...
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Total momentum operator for the KG field
This question pertains to Equation (2.33) in Peskin and Schroeder:
$$
\hat{\vec P}=-\int d^3\!x\,\hat\pi(\vec x)\vec\nabla\hat\phi(\vec x)=\int d^3\!p\,\vec p\,\hat a_{\vec p}^\dagger\,\hat a_{\vec p}
...
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Questions related to conservation of momentum [closed]
I have a related to the conservation of momentum :
The question is: A railroad car is moving along a straight frictionless track. In each of the following cases, the car initially has a total mass (...
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Gauge invariance of a Schroedinger equation for a particle in a box [closed]
Perhaps a bit naive question, but for a particle in a box, e.g. 1D box of width $W$, without any other potentials (e.g., electric, or magnetic) can we raise a question of gauge invariance?
The reason ...
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The Expectation Value of Momentum Operator
So I had found two question based on the title one was talking about momentum operator in bound state and the other was a more general. Where in the first bound state calculation they had related $\...
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Why is the canonical momentum operator for a charged particle not observable in an E&M background?
From the Wikipedia article on the momentum operator (https://en.wikipedia.org/wiki/Momentum_operator#Canonical_commutation_relation) the following operator (in position representation)
$$\hat{\bf{P}} ...
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Electron momentum in a one-dimensional lattice and conservation issue
A one-dimensional lattice is a periodic array of atoms or ions where any two adjacent ions are separated by a fixed distance, the lattice spacing $a$. The Hamiltonian of an electron moving in this ...
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How is the RMS energy of a nucleon in a nucleus of mass number A in its ground state depend on mass number of the nucleus?
So, in my book it's said that the RMS energy of a nucleon in a nucleus of mass number A in its ground state varies as A^(-1/3). Can you please explain how did we arrive at this? Are nucleons ...
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Question related to conservation of momentum [closed]
I have two questions related to the conservation of momentum :
The first one is: A railroad car is moving along a straight frictionless track. In each of the following cases, the car initially has a ...
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Do $p_\mu$ and $\gamma^\mu$ commute?
So I am trying to derive the relation $\bar{u}_{(s)} (\displaystyle{\not}{p} -m)=0$ from the conjugate dirac equation $(i \partial_\mu\bar{\psi}\gamma^\mu+m\bar\psi) = 0$ but I am running into issue. ...
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What went wrong in the following calculation of $\langle p'|[x,p]|p'\rangle$? [duplicate]
We know that $$[x,p]=i\hbar. $$
Consider now the diagonal element in the momentum representation, $$\langle p'|[x,p]|p'\rangle=i\hbar\langle p'|p'\rangle=i\hbar\delta(0).$$
But the LHS = $$\langle p'|...
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Two cars travelling towards each other with the same velocity and different mass. They crash. Which one has the largest acceleration?
Two cars are both moving towards each other with the same initial velocity of 50km/hr. One of the cars weighs 500kg, the other weighs 1000kg. They collide and stick together after the collision, ...
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Wave function square integrable [duplicate]
In quantum mechanics, when showing that the momentum operator is Hermitian operator, we use the fact that the wave function and its derivative go to zero at infinity from the assumption that the wave ...
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Special Relativity - Momentum Calculation [closed]
Recently I have been reading Berkeley Physics Course - Mechanics. In Chapter 12 (page 350 - 352), author gave a very good example that original definition of momentum $P = mv$ is not working by ...
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Why are Coulomb forces on two charges the same?
I wanted to explain to a person knowing some very very basics of physics, why the force of attraction on two charges $Q_1=3nC$ and $Q_2=-1nC$ are the same. Of course my interlocutor thought that $3nC$ ...
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Derivation of Quantum Momentum Operator in Griffiths
I've been reading through Griffith's Intro to Quantum book and can't understand some of the steps in his derivations. The first one is in his proof of time-independence for the normalization of wave ...
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How to justify (mathematically and physically) the total momentum in many-body physics?
If we have a many-body sistem and we study the limit with infinite particles (we may decide for example to have a fixed constant density), I am trying to understand how classical mechanics and quantum ...
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Does the momentum operator applied to a position state vanish?
In quantum mechanics we have
\begin{equation*}
\langle x|p\rangle=C\exp\left(\frac{ipx}{\hbar}\right)
\end{equation*}
where $C$ is a normalization constant.
It follows that
\begin{equation*}
-i\hbar\...
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How to evaluate the action of a fractional differential momentum operator?
I need to understand how a fractional operator works if before being applied on a test function it acts on another (well known)function:
$$(-i\hbar\frac{\partial}{\partial x}\cdot\delta(x))^\epsilon\...
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Proof that if the 3-momentum is conserved then so is energy. (Weinberg's Gravitation and Cosmology)
In section 4 chapter 2 of his book "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity", Weinberg argues that if the 3 momentum is conserved in a '...
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How does the Hong-Ou-Mandel (HOM) effect conserve photon momentum?
HOM is a two-photon interference effect where temporally overlapped identical photons coming perpendicular to a beam splitter must leave it in the same direction.
How is momentum conserved in this ...
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Why does a current loop obey Newton's third but a charged particle doesn't?
My super basic question is, the (magnetic) force between two steady current loops obeys Newton's third but the (magnetic) force between two charges doesn't. This is surprising given that the former is ...
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Replace sum or subtraction of momentum vectors with an equivalent vector
For the diagram, how would I replace the sum or difference of two momentum vectors with an equivalent momentum vector? So, for example in the x-direction:
$$m_e u_e cos\beta = m_1 u_1 cos\beta + m_2 ...
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Time-evolution of momentum eigenstate under harmonic oscillator Hamiltonian
I'm wanting to understand the dynamics of a momentum eigenstate $| p \rangle$ governed by a harmonic oscillator Hamiltonian. Consider $\hat{H} = \hat{p}^2 + \hat{q}^2$. Then inserting a completeness ...
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Motion/momentum of a wave packet
I'm reading Dirac's "Principles of quantum mechanics" right now, being a little confused about the following part: (Chapter V$\S$31: "The Motion of Wave Packets").
He's making the ...
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Confusion in relating conservation of momentum and conservation of energy in a system of particles
Here I have a numerical which caused me confusion , a bullet is fired with a certain velocity horizontally towards a block of the same mass kept on a horizontal surface which is not frictionless , ...
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Momentum in terms of comoving velocity in cosmology
I want to understand why the following relation holds in the context of Cosmology, considering that $m$ is the mass of a particle of the fluid that fills the universe:
$$\vec{p}=am\vec{u}$$
where this ...
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Energy and momenta of a field on a curved manifold
In a curved spacetime with metric $g$, let us have a complex scalar field $\Phi$. The stress energy momentum tensor of the field is defined as,
$$T_{ab} := \frac{-2}{\sqrt{-g}} \frac{\delta S_\Phi}{\...
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Physics of "Getting over it"
So I came across this game called "Getting over it". It is a game where you propell yourself upwards with a hammer, sticking it into various places to keep it in place. My question is, if ...
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Trouble conceptualizing Conservation of Momentum
I just learnt the concept of conservation of momentum, and wanted to make sure my thinking was correct on a toy example.
Question
Suppose you're in a car full of frictionless sand traveling on a ...
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Adjoint of the Dirac equation, and hermiticity of the momentum operator
I'm trying to derive the adjoint of the Dirac equation in standard relativistic quantum mechanics. We have the Dirac equation as follows :
$$(i\gamma^{\mu}\partial_\mu -m)\psi=0$$
To find it's adjoint,...
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When should I use momentum or kinetic energy? [duplicate]
So the basic problem in school we had was "two cars hitting eachother, calculate the speed after hit". We have been taught to use momentum (mv), but why not kinetic energy (0.5mvv)?
So for ...
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How to mathematically prove the balls move at equal speeds after an inelastic collision?
Consider a ball moving at a certain speed. It hits an identical ball at rest. After the collision, both the balls move at equal angles $\theta \ne 90^{0}$ (inelastic collision) with the original line ...
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Determining the direction of the force? [closed]
Consider the above. Why must the force be defined to act upwards rather than acting downwards?
Consider defining the upwards direction as negative and the downwards direction as positive. We then have ...
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2d collisions of perfectly elastic circles with mass
My question is about 2 circles colliding. I can't describe it perfectly, which is part of the reason I'm stuck. Here is a picture.
There are 2 circles. They both have an initial position, velocity, ...
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What is the combined mass of two relativistic particles inelastically colliding into a singular relativistic particle?
A perfectly inelastic central collision of two equal relativistic particles whose kinetic energies are equal to their resting energies results a single relativistic particle (and nothing but it). The ...
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Connection between momentum space derivative and Position operator
The crystal momentum $p_1 =\hbar\cdot k $ and this is defined in the reciprocal momentum, I am guessing this $p_1$ is not a real momentum since the reciprocal space is an imaginary space which we use ...
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Why do we have momentum?
Momentum is the defined as the product of mass and velocity and can be thought as measuring how much motion something has. However, it is not clear to me why we need momentum and why force is not ...
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How come shooter does not receive same energy as bullet (Newton's third law)?
So for example, a bullet weighting 7 g and going out of barrel at 420 m/s has ~617 joules of kinetic energy. So I'd think same would apply to shooter (or his hand specifically) - a 80 kg shooter would ...
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How can you find the final velocity of a ball hitten by a train? [closed]
I want to clarify that I've already seen this question asked here , but I'm interested in how you'd solve it with the conservation of momentum rather with the relativity mechanism of finding the ...
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Why do the eigenvalues of the 4-momentum operator organize themselves into hyperboloids?
Specifically I'm asking for the motivation behind figure 7.1 in page 213 of the QFT textbook by Peskin and Schroeder. In that section they just consider eigenstates of the 4-momentum operator $P^\mu=(...
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