All Questions
Tagged with galilean-relativity homework-and-exercises
26 questions
2
votes
1
answer
168
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Transformation of wavefunction
While learning QM, I was wondering how would the wavefunction of a particle, suppose charged particle, look for different observers moving with respect to each other.
To begin with, let the electric ...
- 457
1
vote
0
answers
90
views
Galilean invariance of Burgers Equation [closed]
I think the following statement is true: if $u$ solves the burgers equation (ie $u$ solves $$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = 0$$ then so does $$u^c = u(x-ct,t)+c.$$ I'...
- 123
0
votes
0
answers
88
views
How can I show that the one-dimensional wave equation (with a constant propagation velocity $c$) is not invariant under Galilean transformation? [duplicate]
The one-dimensional wave equation is given by
- 1
3
votes
3
answers
535
views
Velocity and kinetic energy, violating galilean relativity
I have a toy car and a battery. The barrery has a screen that shows how much energy it has left. Since kinetic energy is proportional to velocity squared, I need 1J of energy to go from 0m/s=>1m/s, ...
- 84
2
votes
1
answer
134
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Time evolution of Galilean boost
I was introduced the generator of Galilean boost $K=mx-pt$.
I was given an Hamiltonian with several particles: $H=\sum_i \frac{p_i^2}{2m_i}+V(|x_i-x_j|)$ where the potential only depends on the ...
- 197
2
votes
0
answers
128
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Invariance of the Schoedinger equation for the Galilean transformation [closed]
Show that the schroedinger e is covariant under the galilean transformation :
$\overrightarrow{r'}=\overrightarrow{r}-\overrightarrow{V}t$
iff the wave fucntion transforms like:
$$\psi^\prime=e^{\left(...
- 189
1
vote
1
answer
800
views
Galilean transformation of the wave equation, derivatives [closed]
So I'm trying to show that when the wave function
$ (-\frac{1}{c^2}\frac{d^2}{dt^2} + \frac{d^2}{dx^2})\phi(t,x) = 0 $
undergoes the Galilean transformation
$ t' = t $
$ x' = x-Vt $
the resulting ...
- 13
2
votes
2
answers
1k
views
Show the Galilean covariance of Schrödinger equation
I'm trying to show the Galilean covariance of the (time-dependent) Schrödinger equation by transforming as follows:
$$
\left\{\begin{eqnarray}\psi(\vec{r},t) &=& \psi(\vec{r}'-\vec{v}t,t),\\ \...
- 1,448
2
votes
1
answer
837
views
Galilean transformation and differentiation
Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
- 341
1
vote
1
answer
1k
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Transformation of the operators $\mathbf\nabla$ and $\partial/\partial t$ under Galilean transformation
I want to know how are the transformations of the operators $\mathbf\nabla$ and $\partial/\partial t$ when the transformation of the Galilean relativity is applied.
This is what I've tried:
Galilean ...
- 454
1
vote
1
answer
1k
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Why are Maxwell's equations not Galilean invariant? [closed]
So i am writing an essay on the conflict between galilean invarience and maxwell's electromagnetism. I am struggling to come up with 3 evidences that they conflict because I have a mediocre ...
2
votes
0
answers
763
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Galilean invariance of the free schroedinger equation [duplicate]
My question follows this question: Naive interpretation of Galilean invariance of the TDSE
Essentially, I'm not sure how to proceed mathematically.
We have the transformations:
$$\begin{cases}x'=x-...
- 454
1
vote
1
answer
422
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Galilean group transformations
My problem is the following:
I have difficulties in answering questions (c), (d) and (e).
For (c) my answer was $\sqrt{x^{2}+t^{2}}$ and yes, the group forms the group of all isometries since the ...
6
votes
2
answers
2k
views
Inonu-Wigner Group Contraction
I am trying to understand how one obtains the Galilean algebra from the Poincare algebra, specifically through the method of central extension. I'm doing this by imposing that the generators of the ...
- 1,062
1
vote
1
answer
342
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Question about Galilean relativity [closed]
If a boat is moving at constant speed relative to water, on a trip between two cities, the ride upstream lasts $t_1=6~h$ and the ride downstream lasts $t_2=3~h$. What time ($t'$) will the boat need to ...
- 332
0
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1
answer
353
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Introduction to Special Relativity Question - Momentum Conservation
I'm currently reading a text for self-study on special relativity, Introduction to Special Relativity by James H. Smith, and I came across a question that I don't see to grasp at the moment.
"Figure ...
- 3
0
votes
0
answers
871
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Galilean transformation of Schrodinger equation and momentum operator [duplicate]
Let
$$
\left.\begin{aligned}
t'&=t\\x'&=x-vt
\end{aligned}\right\} \quad \Longrightarrow\quad \dot{x}'=\dot{x}-v
$$
and therefore $p'=p-mv$.
If $p'=-i\hbar\nabla' $, then $\nabla'=\nabla-iv/\...
- 868
0
votes
1
answer
399
views
Galilean relativity in QM
Intro
I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as:
$$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$
As a reminder the transformation ...
- 705
2
votes
3
answers
2k
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Prove that the spacetime interval is not invariant under Galilean transformations [closed]
The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
- 231
1
vote
1
answer
3k
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Invariance of law of conservation of angular momentum under a Galilean transformation [closed]
Given a reference frame O' moving at a constant speed $\vec{V}$ in relation to another reference frame O, I want to prove that
$\vec{r_{1B}} \times m_1\vec{v_{1B}} + \vec{r_{2B}} \times m_2\vec{v_{...
- 111
0
votes
2
answers
129
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Does it take less time to drop a ball than fire one horizontally (with $90^{\circ}$) [closed]
So I was arguing about this with my friend. If we take two balls and drop one from a certain height H and then fire another one with horizontally with some initial speed from the same height H, which ...
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3
votes
1
answer
308
views
Representations of Galilei group
Show that the operator $U(\alpha, \beta) = e^{i(\alpha \hat{x}^2 + \beta \hat{p}_{x}^2)}$ can represent the space reflection of the 1D Galilei group: $x \to -x; t \to t$.
I don't really know anything ...
- 177
1
vote
0
answers
136
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Galilean Transform
I tried to solve a problem using two different ways and I had some trouble, the problem is:
We define a symmetry transform of the expected value of $\vec{P}$ like this:
$$\langle \psi|\vec{P}|\psi \...
- 103
2
votes
1
answer
2k
views
Generator of Velocity Transformations - Galilean Transformations
Under a Galilean transformation, the coordinates and momenta of any system transform as:
$$ t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v $$
where $\vec v$ is ...
- 379
2
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0
answers
456
views
Jacobian matrix of Galilean transformation
If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation?
2
votes
2
answers
1k
views
Velocity of an object undergoing homogenous acceleration
So I was considering the following problem within the context of Special Relativity:
Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
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