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Tagged with galilean-relativity schroedinger-equation
15 questions
3
votes
0
answers
32
views
Galilean boost operator for quantum multi-particle system
If I have a two particle system with with a potential of form $V(x_1,x_2)$, is it possible to apply the galilean boost operator to only a single coordinate? Essentially, is it possible to move only a ...
- 331
0
votes
0
answers
33
views
Galilean boost and translation in field theory
I am reading some literature which is considering translations and boosts in field theory. The reference is Construction of Lagrangians continuum theories, Markus Scholle, 2004, The Royal Society. I ...
1
vote
1
answer
683
views
Differential Equation that combines QM with Galilean relativity
In Galilean Relativity if there are two objects, the initial positions of the objects, their masses, and the forces acting on the objects is not enough to uniquely determine where the objects will be ...
- 2,021
3
votes
1
answer
328
views
Galilean covariance of the Schrödinger equation without choosing a representation
The most general form of Schrödinger equation is
$$i \hbar \frac{d}{d t}\Psi(t) = H\Psi(t) \tag 1,$$
where $\psi(t)$ is an element of a Hilbert space $\mathcal H$ (not necessarily $L^2$), and $H$ is a ...
- 757
6
votes
2
answers
729
views
Why is the phase of a matter wave not Galilean invariant? And what does this say about the Schrödinger equation? [duplicate]
Matter waves are not Galilean Invariant
Consider a non-relativistic freely-propagating matter wave in an inertial frame $\Sigma'$ moving along the $x'$-direction with kinetic energy $E'=1/2m_0v'^2$, ...
- 1,826
2
votes
1
answer
912
views
Galilean invariance of Schrödinger equation [closed]
I'm trying to prove that if $\psi (\mathbf r, t)$ satisfies
$$
i\hbar \frac{\partial\psi}{\partial t}(\mathbf r, t) =
-\frac{\hbar^2}{2m} \left( \nabla-\frac{iq}{\hbar} \mathbf A \right)^2\psi(\...
- 1,999
2
votes
0
answers
128
views
Invariance of the Schoedinger equation for the Galilean transformation [closed]
Show that the schroedinger e is covariant under the galilean transformation :
$\overrightarrow{r'}=\overrightarrow{r}-\overrightarrow{V}t$
iff the wave fucntion transforms like:
$$\psi^\prime=e^{\left(...
- 189
3
votes
1
answer
301
views
Differences between the conformal group and the Schrödinger group?
Facts:
The Maxwell (free) equations (4d) are invariant under the 15 dimensional conformal group.
The free Schrödinger equation in 3d is invariant under the 15 dimensional group "called" Schrödinger ...
- 6,727
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:
$$
\left\{\begin{eqnarray}\psi(\vec{r},t) &=& \psi(\vec{r}'-\vec{v}t,t),\\ \...
- 1,448
3
votes
1
answer
1k
views
Derive the Lagrangian that yields the free Schrödinger's equation from Galileian Invariance
The Lagrangian Density $$L(\Psi, \Psi^*)=i \hbar \dot{\Psi} \Psi^* + \frac{\hbar^2}{2m} \Psi \Delta \Psi^*$$ will yield the schroedinger equations for $\Psi$ and $\Psi^*$. Can we derive this ...
- 6,955
2
votes
0
answers
763
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Galilean invariance of the free schroedinger equation [duplicate]
My question follows this question: Naive interpretation of Galilean invariance of the TDSE
Essentially, I'm not sure how to proceed mathematically.
We have the transformations:
$$\begin{cases}x'=x-...
- 454
0
votes
0
answers
871
views
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
10
votes
1
answer
727
views
Can Schroedinger equation be derived from the unitary representation of Galilean group?
I have been trying to understand quantum mechanics as a unitary representation of spacetime symmetries.
My first question is: Can Schroedinger equation be derived from the unitary representation of ...
- 1,110
3
votes
1
answer
2k
views
Naive interpretation of Galilean invariance of the TDSE
I was told today by someone smarter than myself that the time-dependent Schroedinger equation in one dimension was invariant under a Galilean transformation of $(x,t)$, namely under
$$\begin{cases}x'=...
- 576
28
votes
4
answers
23k
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Galilean covariance of the Schrodinger equation
Is the Schrodinger equation covariant under Galilean transformations?
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:...
- 3,802