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Results tagged with linear-systems
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user 27732
A linear system is a mathematical model of a system based on the use of a linear operator. A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions.
2
votes
What is the difference between a linear and a non-linear perturbation?
I would tend to agree with you that this (commonly used) language is somewhat misleading. A perturbation is just a perturbation, "linear" and "non-linear" are words that describe the methods used to u …
- 55.3k
0
votes
How translation, rotation and translation plus rotation of a body can be define particle by ...
Let's say the rod has mass $M$ and length $L$, and the density is uniform. Let's imagine breaking the rod into $N$ mass elements each of mass $m=M/N$ and length $\ell=L/N$. Then the equation of motion …
- 55.3k
2
votes
Accepted
Is there a "measure of nonlinearity" that can be measured when testing quantum mechanics?
The post-Newtonian expansion in GR is an expansion in powers of $1/c^2$. You can derive this expansion from an effective field theory approach in which every possible term consistent with symmetries i …
- 55.3k
1
vote
Accepted
How to check that any linear combination of solutions is itself a solution to the time-depen...
First, note that the time dependent Schrodinger equation is
$$
i \hbar \frac{\partial \Psi}{\partial t} = \hat{H} \Psi
$$
Let's suppose like in your example that
$$
\Psi = c_1 \psi_1 e^{-i E_1 t / \hb …
- 55.3k
2
votes
Accepted
Can a non-unitary process be made unitary using a transformation or by expanding the phase s...
But if that's not the case, is there a way to make the time evolution unitary, either by doing a variable transformation (i.e., 𝐱=𝐵𝐲
for some invertible 𝐵
)
A mathematical change of variables ca …
- 55.3k
2
votes
Accepted
Is QFT linear with respect to superposition of multi-particle states?
There is no distinction between quantum field theory and quantum mechanics in terms of how to answer this question. You can think of QFT as a specific application of quantum mechanics here.
The Schrod …
- 55.3k
7
votes
Are there any nonlinear Schrödinger equations?
Quantum mechanics depends on the Schrodinger equation being linear. It is perfectly possible to invent a model with a nonlinear Schrodinger equation describing the wavefunction and ask if it describes …
- 55.3k
1
vote
Possibility of complex EM waves
Mathematically, you can consider complex valued solutions of Maxwell's equations.
Physically, it doesn't make sense to consider a complex electric field. Consider the equation for the Lorentz force
$$ …
- 55.3k
8
votes
Accepted
How does the linearity of the Schroedinger equation reflect the interactions?
There are different equivalent formulations of quantum mechanics, and how an interaction is represented in each formulation is different.
In the Schrodinger picture, operators are time independent an …
- 55.3k
3
votes
Accepted
Understanding linearity of Maxwell's equation compared to non-linarity of GR
This is a good question because it points out thing people say ("Maxwell's equations are linear") which is true but can be easily interpreted incorrectly.
First, just to clarify, a set of differential …
- 55.3k
1
vote
Accepted
Conjecturing the homogeneous solution of a $2^{nd}$-order constant coefficients ODE - why co...
The original problem is to find a real-valued solution, with two real-valued integration constants. The trick he is using is to generalize the problem to finding a complex-valued solution, with two co …
- 55.3k