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3
votes
2answers
266 views

Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
18
votes
5answers
2k views

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 ...
2
votes
2answers
3k views

Is squared motor gearbox ratio proportional to inertia ratio?

I read an interesting article http://m.machinedesign.com/news/motor-sizing-made-easy It is very interesting, but I can not follow the 2nd last paragraph. I don't understand why it is true. ...
8
votes
4answers
3k views

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 ...
9
votes
3answers
646 views

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 ...
3
votes
1answer
2k views

Is the universe linear? If so, why?

Simple question, I'm trying to build a quantum memory system that utilizes the superposition principle to model specific phenomenon I am trying to predict, anyways, my question is this. Is the ...
5
votes
4answers
26k views

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 ...
5
votes
1answer
721 views

Why doesn't amplitude affect the speed of sound?

I understand why amplitude doesn't affect the speed of the sound AFTER the 'leading compression'. The extra force provided on one stage of the cycle is countered on the other stage. But shouldn't the ...
9
votes
1answer
1k views

Matrix solution of an equivalent resistance circuit problem

Start with a set of points $x_1, x_2, \ldots$ that are connected by wires with some resistance. Represent the resistance by a conductance matrix (conductance being one over the resistance), where ...
5
votes
3answers
370 views

The ubiquitous Planewave Ansatz

In physics, the planewave ansatz (meaning: an educated solution guess) is very ubiquitously used, when solving differential equations, in different domains of physics. E.g. to solve the dispersion ...
3
votes
2answers
13k views

How to get “complex exponential” form of wave equation out of “sinusoidal form”?

I am a novice on QM and until now i have allways been using sinusoidal form of wave equation: $$A = A_0 \sin(kx - \omega t)$$ Well in QM everyone uses complex exponential form of wave equation: $$A ...
-1
votes
2answers
209 views

Linearity in Quantum Mechanics that make superposition possible

As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
1
vote
0answers
366 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate ...
0
votes
1answer
59 views

Why superposition is useful just for linear functions?

I saw a problem which said that we have a bar between two walls and we increase the temperature. and as you know walls push a force to the bar so the length of it does not change. in the solution I ...
0
votes
4answers
2k views

What does superposition mean in quantum mechanics?

What does superposition mean in quantum mechanics? When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$. But when ...