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12
votes
1answer
560 views

What quantum phenomena violate the superposition principle in electromagnetism?

On page 11 of the 3rd edition of Electricity and Magnetism by Edward M. Purcell and David J. Morin it says: "we know of quantum phenomena in the electromagnetic field that represents a failure of ...
0
votes
1answer
109 views

Solution of the coupled non-linear oscillators by using perturbation theory [closed]

The integration shown here, $$∫_{-\infty}^{+∞}x^r\mathrm{Exp}[−x^2]\mathrm{H_n}^2[x]\mathrm{d}x,$$ appears when we try to calculate the spectrum of the perturbed non-linear oscillators by using ...
2
votes
2answers
128 views

Is non-linear quantum mechanics possible?

Say we have a state vector $|A\rangle$. Is it possible to have a theory where the evolution of $|A\rangle$ depends on the vector $|A\rangle$ itself? e.g. $$ i\frac{\partial}{\partial t} \psi(t) = \...
0
votes
1answer
67 views

quantized energies for a particle in a non-linear potential

Okay, so the question i'm trying to solve is to find the quantized energies for a particle in the potential: $$V(x)=V_0 \left ( \frac{b}{x}-\frac{x}{b} \right )^2$$ for some constant b. I used the ...
0
votes
0answers
122 views

Two E-fields and two energy levels create infinite frequencies?

In this paper it says that for a two-level system excited by two fields: $$ V_{ab} = -\mu_{ba} E_1 e^{i \omega_1 t}+ E_3 e^{-i \omega_3 t}$$ "In steady state the off-diagonal density-matrix ...
1
vote
1answer
99 views

How do nonlinear phenomena arise from linear theories

How is it possible that linear theories, for example maxwells equations or the schroedinger equation, produce nonlinear physics?
0
votes
1answer
79 views

Is linearity of quantum theory important for existence of quantum gravity?

Kiefer (2014) claims that, "It is, in fact, the superposition principle that points towards the need for quantizing gravity." Moreover, Kiefer (2009) stresses that, "The only assumptions are ...
2
votes
0answers
322 views

Trial function in variational principle - why do we choose this ansatz?

I am reading this paper right now and I cannot understand the intuition behind their choice of ansatz in the variational principle. Specifically this passage on the second page of the paper puzzles ...
1
vote
3answers
190 views

Are all the quantum based equations linear?

I dont know much about the subject, but the wave equations (classical and modern) as well as classical equations of motion all seem to be inherently linear differential equations. Presumably this also ...
20
votes
3answers
3k views

Is the universe non-linear?

First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer. Theories like General Relativity or QFT, which are believed to be quite ...
2
votes
3answers
749 views

Example of non-linear time evolution in quantum mechanics

Preamble: I am a mathematician and not a physicist. From what little I know about quantum mechanics, Schrödinger's equation is a linear PDE that describes the time-evolution of a system. In general ...
11
votes
3answers
493 views

No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
-1
votes
1answer
134 views

Are there nonlinear models of quantum mechanics which forbid superluminal signaling?

What would a nonlinear model of quantum mechanics which forbids superluminal signaling look like? Of course, a nonlinear $\psi$-ontic theory with entangled states could have superluminal effects upon ...
3
votes
5answers
400 views

How does non-linear behaviour arise from the inherently linear QM framework?

Quantum mechanics is a linear theory, living in a Hilbert space with built-in linearity. It has even been argued that introducing non-linearity in the quantum theory would allow for superluminal ...
6
votes
2answers
395 views

Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction $\...
7
votes
3answers
2k views

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics?

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
0
votes
1answer
618 views

Inhomogenous Schrödinger equation

Please help me out in solving this inhomogeneous Schrödinger equation in cylindrical co-ordinates [You may suggest if I have to go for mathematics]: $$ \ddot R + \frac1r\dot R+\left(b^2-d^2-\frac{a^2}...
4
votes
2answers
669 views

What are the solution spaces of Nonlinear Schrödinger equations?

As we know, the solution space of Schrödinger equation is a Hilbert space, however, what about it of Nonlinear Schrödinger equations such as $$i\partial_t\psi=-{1\over 2}\partial^2_x\psi+\kappa|\psi|^...
4
votes
4answers
361 views

Non linear QM and wave function collapse

I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably ...
2
votes
1answer
278 views

Examples of piecewise smooth dynamical systems [closed]

I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow ...
8
votes
2answers
2k views

Nonlinear dynamics beneath quantum mechanics?

Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered. ...
15
votes
5answers
2k views

Could the Schrödinger equation be nonlinear?

Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity (QG) be ...
22
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 ...