The tag has no usage guidance.

learn more… | top users | synonyms

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 ...
0
votes
1answer
21 views

Does object traversing in linear motion have a constant bearing rate?

If an observer is moving at a constant rate and constant direction and another object traverses in front of the observer and is also moving in a fixed direction at a constant rate, will the bearing ...
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
1answer
26 views
0
votes
0answers
30 views

Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
0
votes
2answers
49 views

Why is a circuit of linear elements itself linear?

A resistor's voltage is proportional to it's current. V=iR. And a source maintains a constant voltage or current. So these are linear, time independent relations. If I put combinations of them in a ...
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. ...
3
votes
0answers
68 views

Linear Classical Field Theories: a Mathematical Classification

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
4
votes
1answer
88 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
3
votes
3answers
59 views

Why is response of system same frequency as driving force frequency

Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ...
-1
votes
1answer
146 views

Meaning of Eigenvalues/Eigenvectors of a linear system of equations

I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other ...
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 ...
5
votes
0answers
54 views

Lyapunov stability of circular orbits

I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
4
votes
2answers
707 views

Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
2
votes
1answer
104 views

Physical interpretation of the canonical scalar product in linear dynamics

Consider a unforced, undamped, linear mechanical system with a finite number of degrees of freedom. Its (second order) dynamical equations can be gathered in a matrix equation $$M\ddot X + K X=0$$ ...
2
votes
2answers
299 views

Principle of superposition and QED

For finding a net force on a charge when it is in influence of many charges we simply do vectorical addition of all individual interaction of that charge with others. That's what is principle of ...
4
votes
1answer
1k views

What is the Laughlin argument?

The fundamental question is Why is Hall conductance quantized? Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the ...
2
votes
1answer
148 views

General second order system and mass spring damper in control theory

I am studying control theory and most textbooks and web resources define a general second order system in the $s$ domain as $$ G(s) = \frac{\omega_n^2}{s^2+2\,\zeta\,\omega_n\,s+\omega_n^2} \, .$$ ...
0
votes
0answers
27 views

Initial conditions for second order ODE with complex stiffness

I tried this on Math Stack Exchange. I'm trying to find initial conditions to ensure systems of the form stay bounded $$\ddot{x}_i+\sum_{j=1}^N k_{ij} x_j = 0, \quad k_{ij} \in \mathbb{C}.$$ For ...
0
votes
0answers
84 views

Kirchoff's circuit law matrix representation

A couple of recent Kirchoff's law questions with wacky geometries got me thinking. "Solving" any circuit that consists only of resistors and e.m.f. sources can be reduced to solving a linear system of ...
-1
votes
2answers
208 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 ...
0
votes
3answers
460 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
1
vote
1answer
94 views

Variable Gear System [closed]

I have a variable speed gear system with 4 primary parts. I need to find the relationship between input rotational speed (wi) to output rotational speed (wo). Fig. 1 shows three of the primary ...
1
vote
1answer
106 views

Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?

Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
0
votes
1answer
346 views

Superposition in classical Mechanics

I watched a video in YouTube solved these problem using superposition First he fixed the bottom rope and found the accelearations Second he fixed the upper pulley and found the accelerations Third ...
2
votes
2answers
4k views

Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate]

Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean: ...
1
vote
2answers
50 views

What dynamical system could this $\dot y = \alpha(y-\lambda), y\geq \lambda$ equation describe?

Just out of curiosity, can anyone identify electrical, mechanical, chemical, etc process that is governed by a differential equation of the form $$\dot y = \alpha(y-\lambda), y\geq \lambda$$ where ...
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 ...
0
votes
0answers
85 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
5
votes
3answers
369 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
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?
1
vote
1answer
59 views

What makes a system linear?

Lately I have been interested in Image Processing, and I started by following this course: https://class.coursera.org/digital-001, which is quite awesome in my opinion. But in weeks 2, Linear ...
1
vote
2answers
258 views

Would magnetic flux be necessary for analogous systems?

I learned about the analogousness between mechanical and electrical systems a few months back (with the help of Feynman). Yesterday, my professor was lecturing about this topic, when she told that ...
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 ...
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 ...
1
vote
0answers
156 views

Is strictly harmonic 2D lattice made of Hooke springs possible?

If we connect a set of point masses in a 1D lattice with Hooke springs and consider longitudinal oscillations, we'll have a strictly harmonic system, for which there exist eigenmodes and the frequency ...
2
votes
1answer
309 views

Principle of Superposition for driven oscillator

So I understand the the Superposition Principle states that all the forced oscillations, as determined by multiple external forces, are to be added up in order to get the entire solution. However, ...
0
votes
1answer
278 views

Superposition theorem

Is superposition theorem applicable for circuits having semiconductor components like diodes, transistors, etc.?
1
vote
2answers
191 views

Physics and Linear Differential Equations

Why in physics, most of the physical systems are modelled by linear differential equations?
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 ...
3
votes
0answers
89 views

Multiple meanings of polarizability?

There's a concept in linear response theory called the polarizability $\chi$ $$\tag{1} \rho_{ind}=\int \chi(\vec{r},\vec{r}',t-t') V_{ext} \: d\vec{r}' dt' $$ where $\rho_{ind}$ is the induced charge ...
2
votes
1answer
188 views

Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
3
votes
2answers
260 views

“Complex Variables Method” in Diff. Eq. - Justification and physical meaning?

A common method of simplifying calculations that involve differential equations - particularly involving oscillation - is to replace $\cos(\theta)$ with $e^{i \omega t}$, evaluate, and then take the ...
9
votes
3answers
643 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 ...
0
votes
0answers
102 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the ...
1
vote
2answers
160 views

Linear quantization in quantum electrodynamics?

This is a continuation of this question. What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.
2
votes
2answers
166 views

Undamped oscillations. Why is the solution a linear combination of $\sin()$ and $\cos()$?

$ma = mg - cx$, where $x(0) = x_0 = 0$ is the position in which there is no tension in the rope. $dx/dt = v_0$ for $t = 0$; $v_0$ is a known constant. The discriminant of the characteristic ...
1
vote
0answers
365 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
168 views

Microphones, Loudspeaker and their analogies to spring mass system

I have just started studying Microphones and Loudspeakers. I need a good text to refer which can explain their mechanical analogies with simplicity and basics too.
2
votes
3answers
83 views

Solving systems of equations in dynamics

I have an exam in two days for first year university physics. Often for dynamics problems, I am required to solve algebraic systems of equations by hand, and this can be very daunting. When I see ...