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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If photons have no mass, how can they have momentum?
As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects ...
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How does the momentum operator act on state kets?
I have been going through some problems in Sakurai's Modern QM and at one point have to calculate $\langle \alpha|\hat{p}|\alpha\rangle$ where all we know about the state $|\alpha\rangle$ is that $$\...
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How can momentum but not energy be conserved in an inelastic collision?
In inelastic collisions, kinetic energy changes, so the velocities of the objects also change.
So how is momentum conserved in inelastic collisions?
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What's the deal with momentum in the infinite square well?
Every now and then a question comes up about the status of the momentum operator in the infinite square well, and while we have two good answers on the topic here and here, I'm generally not satisfied ...
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How can I solve this quantum mechanical "paradox"?
Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$.
The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
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What is a rocket engine thrusting against in space?
I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut ...
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What's wrong with this derivation that $i\hbar = 0$?
Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore $$\...
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How does one account for the momentum of an absorbed photon?
Suppose I have an atom in its ground state $|g⟩$, and it has an excited state $|e⟩$ sitting at an energy $E_a=\hbar\omega_0$ above it. To excite the atom, one generally uses a photon of frequency $\...
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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?
I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance.
Am I ...
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Why does the amount of energy transferred depend on distance rather than time? [duplicate]
The change in energy of an object can be determined by the work equation, where work is the change in energy:
$$ W = F \cdot d $$
I conceptualize the transfer of energy as simply a series of small "...
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Neutrino Oscillations and Conservation of Momentum
I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a ...
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Does the canonical commutation relation fix the form of the momentum operator?
For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar. $$
Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
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Can linear momentum be conserved before and after collision in the presence of an external force?
I'm a physics tutor for 11th and 12th grade students. I taught my students that momentum is conserved only when the net external force on the system is zero. But in the books we are following, ...
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Hermiticity of Momentum Operator (matrix) Represented in Position Basis
I read that the momentum operator, $\hat P$ should be Hermitian (some would say by QM postulate). That makes perfect sense when it is represented in the momentum (p) basis: $\hat P =\int_{-\infty}^{\...
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Does leaning (banking) help cause turning on a bicycle?
I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ...
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