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.
Questions tagged [linear-systems]
313 questions
32
votes
9 answers
What is the most appropriate mathematical theory for electrical circuits?
What exactly are electrical circuits as mathematical objects?
It seems quite intuitive to me, that they are geometric realization of some graph with some additional structure.
Another thing I notice is that application of KVL and KCL together turns…
Clemens Bartholdy
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31
votes
5 answers
Linearity of quantum mechanics and nonlinearity of macroscopic physics
We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are the physics points of connection between the two…
Andy Bale
- 2,017
29
votes
6 answers
Do all waves of any kind satisfy the principle of superposition?
Is it an inherent portion of defining something as a wave?
Say if I had something that was modeled as a wave. When this thing encounters something else, will it obey the principle of superposition. Will they pass through each other?
JobHunter69
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21
votes
5 answers
Is there any fundamental reason why acceleration is a linear function of external forces?
Perhaps a trivial question, but it is something which I couldn't ever grasp ever since beginning physics. Why exactly should Newton's second law be linear in application of all the external forces?
For example, suppose I have a spring oscillating…
Clemens Bartholdy
- 8,309
19
votes
4 answers
In classical physics (classical electrodynamics), why linearity of Maxwell's equations prevent interaction of electromagnetic waves?
In classical physics (classical electrodynamics), electromagnetic waves don't interact. In quantum mechanics, they could. In this article on light-by-light scattering:
https://arxiv.org/abs/1702.01625
, the introduction states that there is a…
18
votes
3 answers
What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?
I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form
$$f(x) = Ae^{i (kx - \omega t)},$$
using complex…
CherryGot
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16
votes
5 answers
Why is the Principle of Superposition true in EM? Does it hold more generally?
In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly?
Does it have any limit of applicability or is it a fundamental property of nature?
quark1245
- 1,422
15
votes
4 answers
Transverse Magnetic (TM) and Transverse Electric (TE) modes
I'm reading and working my way through "Plasmonics Fundamentals" by Stefan Maier and I've come across a step in the workings that I'm struggling to understand when working out the electromagnetic field equations at a dielectric-conductor interface.…
Tom
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15
votes
3 answers
Why are so many energies represented by $\frac{1}{2} ab^2$?
Why are so many energies in our universe mathematically represented by the equation $\frac{1}{2}ab^2$.
For example:
Kinetic energy $$\frac{1}{2}mv^2$$
Energy stored in a capacitor $$\frac{1}{2}CV^2$$
Energy stored in an inductor…
Shailendra Sorout
- 185
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14
votes
6 answers
What are the different methods for a resistor circuit that isn't parallel or series?
What are the different approaches to determine the equivalent resistance of nontrivial resistor networks in general, that cannot be reduced by the usual series and parallel rules? (The diagram below is just one the simplest examples of such a…
Carl Brannen
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12
votes
3 answers
Can the Kramers–Kronig relation be used to correct transfer function measurements?
In experimental physics, we often make measurements of linear transfer functions; these are complex-valued functions of frequency. If the underlying system is causal, then the transfer function must be analytic, satisfying the Kramers-Kronig…
nibot
- 9,691
12
votes
3 answers
Where does the use of tensors to describe orientation dependence of physical phenomena arise from?
In the context of anisotropy, I have often read that the use of a rank 2 tensor is "a model". But what is the idea behind this choice? Can anyone describe in what sense the use of tensor in this context is a "model"?
Giulia
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12
votes
1 answer
Is the universe linear? If so, why?
I'm trying to build a quantum memory system that uses the superposition principle to model specific phenomenon I am trying to predict.
Is the universe linear? The superposition principle would apply in all cases if the universe is linear, which…
marscom
- 355
11
votes
3 answers
Why are operators in quantum mechanics always linear?
After looking around in the internet, I could not find a sufficient proof how every operator in QM has to be linear. Many sources claim that the linearity of the Schrödinger equation implies that, however I was not able to find a proof for this.
I…
Karolex
- 408
11
votes
4 answers
Are there any nonlinear Schrödinger equations?
The 1D Schrödinger equation reads:
$$\frac{\partial \Psi}{\partial t}=\frac{i\hbar}{2m}\frac{\partial^2 \Psi}{\partial x^2}-\frac{i}{\hbar}V\Psi.$$
Now, generally we have $V=V(x)$ (or it dependending on any other number of real variables). But…
agaminon
- 4,386