Quantum Definition and 999 Threads

First, the inverse quantum Fourier transform is ##\left | k \right > =\frac 1 {\sqrt {2^n}} \sum_{j=0}^{2^n-1} e^{-2 \pi ijk / 2^n} \left | j \right >##, and it is equal to ##\left | k_1 , k_2 , \dots , k_n \right > \rightarrow \frac { \left ( \left | 0 \right > + e^{-2 \pi i 0.k_n} \left...

In Quantum Mechanics, the position (or momentum) variable is quantized. I define "quantization" as promoting a variable into a probability distribution. For example, with the double slit experiment, the classical assumption that the position/path of a particle is "unique" cannot explain...

In Quanta Magazine there is article on this link...

Summary: A book about problems of quantum computation? I remember that there is a book containing many problems of quantum computation, but I can't find the page or post now. I have hard time learning quantum computation. Thus, I want to try to solve problems in order to get a solid...

What are the best books on QT Foundations out there? This seems to be a difficult question which has very different answers depending on who you happen to ask. There seem to be at least two different levels, e.g. intermediate texts and advanced texts, with a very wide gap in between, which is...

Let’s say to the average Astronomer conducting research; generalizing the research to “astronomy” ; which would be more useful for the “average” Astronomer on a day to day basis: Quantum Mechanics or General Relativity? Obviously most are, but which so more? Which would be referred to more?

I started with the first of the relevant equations, replacing the p with the operator -iħ∇ and expanding the squared term to yield: H = (-ħ^2 / 2m)∇^2 + (iqħ/m)A·∇ + (q^2 / 2m)A^2 + qV But since A = (1/2)B x r (iqħ/m)A·∇ = (iqħ / 2m)(r x ∇)·B = -(q / 2m)L·B = -(qB_0 / 2m)L_z and A^2 =...

Summary: Finding state at t=0, energy values and more So this is my first question in quantum mechanics (please understand). 1. So we have a system, and to describe the state of the system we have to measure, A is an hermitian matrix, that each physical measurable quantity has. To find the...

Hi everyone, I am following along with the MIT OCW quantum optical communication course. I have a question about this chapter, concerning the linear attenuators and amplifiers. Specifically, the chapter mentions that they are not going to get ##\rho_{out}##, but I am interested in this. More...

Friction is commonly thought to arise from the electromagnetic forces of the atoms at the boundary between two surfaces in contact. However it occurs to me that, in addition to charge quanta, there are also mass quanta present in this system and they could very well play a role. Now, I'm just...

In the double-slit experiment when a detector was placed before the two slits, a 2 strip pattern was produced after the two slits. When there was no detector placed before the two slits, a different pattern was produced after the two slits. Why does the presence of a detector before the two...

Which of these premises is impossible or incorrect according to our current understanding of quantum entanglement? Given 2 entangled particles, p1 and p2: Observing paired particle p1 induces a change in spin on paired particle p2. There a way of detecting a change in spin on particle p2...

Hi. After learning quantum computation for months, it fascinates me. Quantum computation expands my view about computational methods. I believe that many future achievements can be obtained from quantum computing, especially the combination of AI and quantum computation. Meanwhile, I think...

I have been asked to draft a (informal) research proposal for a PhD thesis. I have some background in quantum information and my interests are leaning towards the AdS/CFT correspondence. I was wondering if you could suggest a few (preferably recent) theory papers at the junction of quantum...

Quantum Jumps are predicted using microwave monitoring. Weird. https://phys.org/news/2019-06-physicists-schrodinger-cat.html

What does quantum physics say about the simulation hypothesis?

Hello, I have two questions into one. First I would like to know what books are considered the best to introduce the theory of quantum dots, so for example with the k.p method, tight-binding, empirical pseudopotentials, and other techniques, analytical derivations, optical properties, band...

Becker et al. 2019, Asymmetry and non-dispersivity in the Aharonov-Bohm effect The paper is open access and published in Nature Communications.

See Peter Shor's comments here and here and Urs Schreiber's comments here.

I think the effective action should make sense also in Quantum Mechanics, not only in QFT. But I have never seen described in a QM book as such. Could there be a QM book that uses effective actions? Or maybe in QM effective actions are called another name? I think effective actions in QM could...

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Summary: Search to compute gain of a quantum well. Stuck with maths or programming. Hi everyone ! For a personal project, I search to compute the optical gain occurring on a semiconductor quantum well. I have based my calculations on a paper called Investigation and comparison of optical gain...

My attempted solutions was, for example let's say we have 4 atoms, and if i ask the oracle about any two atoms that are connected by edge, i can narrow done some possibilities to two atoms. I'm still not sure where i am going with my solution, but if any of you can think this through and come up...

I'd like to point to the book The Philosophy of Quantum Mechanics by C. Friebe et al., Springer 2018. It contains many topics usually underrepresented in foundational discussions of quantum physics, in chapters on many-particle systems and quantum field theory. It also has in its last chapter a...

Summary: Does the "problem of time in quantum mechanics" go for Lorentz-invariant quantum mechanical theories like QED? Everything I read about "the problem of time in quantum mechanics," i.e. absolute time in QM clashing with relativity's relative time coordinate and relativity of...

In Nielsen's book, the chapter of quantum circuits does not describe explicitly any procedures to design a circuit. For example, given the matrix of Fredkin gate, ##\begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1...

Firstly, I don't know in which Picture this equation holds (if I hadn't missed some words in the previous text...). I think it may be the Heisenberg Picture. But if it is, the rest target is to prove $$\frac{i}{\hbar}[H_R+H_{FR},(a^\dagger) ^ma^nO_A]=\langle\frac{d}{dt}((a^\dagger)...

I'd like to draw attention to a very recent paper by Jürg Fröhlich, a well-known mathematical physicist from the ETH Zürich. It starts out as follows: Section 2 is titled ''Standard formulation of Quantum Mechanics and its shortcomings''. Surely @vanhees71 has very convincing reasons why this...

Introducing the spacetime spherical symmetric lattice, I use the following notifications in my program. i - index enumerating the nodes along t-coordinate, j - along the r-coordinate, k - along the theta-coordinate, l - along the phi-coordinate. N_t - the number of nodes along t-coordinate. N_r...

In a book it says that "we know of quantum phenomena in the electromagnetic field that represents a failure of superposition,seen from the viewpoint of the classical theory." I want to about what quantum phenomena is he talking about? This was from the page 11 of the book Electricity And...

I'm interested in quantum programming. So far I've managed to use Java and Python inside Datamelt computation project for physics simulations and for various statistical plots. Now I want to make a simple code that illustates quantum computing, and maybe even to visualize its principles (for...

In analogy to classical mechanics, I thought a good definition to "What does "solving a quantum mechanics problem" mean?" was to give the propagator (aka the Green function, or the 2-point correlation function): In classical mechanics, solving a problem means to give the path of the particle...

This is a fascinating discussion. I know some people don't want to debate this or they can't debate it but the truth doesn't care about your feelings. This isn't speculative, it's backed by Scientific research. First paper. Is Spacetime an Error Correcting Code. Published in the Journal of High...

Other than with black holes, are there any other natural ways that quantum information can be lost, and thus jeopardize quantum determinism?

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I'm writing a short story about the hero having the ability to control quantum probability. First. Is there any sci-fi novel that explores the ability to control it? Can it imitate telekinesis for example the person focusing on "left" direction whereby the wave function probability would...

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Problem Statement: See below Relevant Equations: 2D density of states ##g\left(E \right)=\frac{m^{*}}{\pi\hbar^2}## Fermi energy in a quantum cascade laser ##E_{F}=E_{i}+k_{B}Tln\left[exp\left(\frac{\pi\hbar^2n^{2D}}{k_{B}Tm^{*}} \right)-1\right]## I've been stuck on this problem for a few...

I am confused about the vector notation of quantum states when I have a 2 qubit system. For 1 qubit, I just write l1> = (0 ;1 ) for representing 1, and l0> = (1;0) for representing 0. Dirac notation is straightforward However when it comes to representing two qubits in linear algebra I...

I am currently studying this paper on quantum synchronization. The first page gives an introduction to synchronization and the basic setup of the ensembles in the cavity. My query is on the second page where the following statements are made. Can anyone see why the implication is that all...

I've read that ##\left | \psi \right > =cos \frac \theta 2 \left | 0 \right > + e^{i \phi} sin \frac \theta 2 \left | 1 \right >##, and the corresponding point in the Bloch sphere is as the fig below shows. I think ##\left | 0 \right >## and ##\left | 1 \right >## are orthonormal vectors...

As I understand the delayed-choice quantum eraser experiment, first performed by Kim in 1999, entangled photons are used to determine which-way data, and the which-way data is obtained by virtue of where the entangled particles land, as opposed to using a measuring device that may be collapsing...

From the proceedings of Group32, the 32nd International Colloquium on Group Theoretical Methods in Physics (9–13 July 2018, Prague): https://iopscience.iop.org/article/10.1088/1742-6596/1194/1/012097 M D Sheppeard Abstract: A physical approach to a category of motives must account for the...

Hi everyone! Sorry for the bad english! Paper: https://arxiv.org/abs/1902.05080 I guess I understood the experiment until the moment Alice and Bob chooses to measure A0(B0) or A1(B1). I guess it's kind of straightforward that without a bell state measurement with photon alfa(beta) and photon...

For my own understanding, I am trying to computationally solve a simple spinless fermionic Hamiltonian in Quantum Canonical Ensemble formalism . The Hamiltonian is written in the second quantization as $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ In the canonical formalism, the density...

I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the...

Hello, I know we have the parity operator for inversion in quantum mechanics and for rotations we have the exponentials of the angular momentum/spin operators. But what if I want to write the operator that represent a reflection for example just switching y to -y, the matrix in real space...

Hello, In Griffiths Intro To Quantum (second edition) example 4.3 page 180 ... Calculating the expectation of <Sx>, equation 4.164. I'm sure I am wrong, but it seems like after using Euler's for the e^i terms there should be 2cos(yB0t)'s terms. I agree the sin's cancel (After using Euler)...

Quantum fields have wave functions that determine a particle position in space. It solves non-locality, double-slit paradox, tunnel effect, etc. What if the wave function is also in time? Won't it solve the breaking of causality at quantum level? (Delayed Choice/Quantum Eraser/Time) Not much...

By the Wigner theorem, symmetries transformations are implemented by operators ##\hat{U}## that are unitary or antiunitary. This is what is written in most books. But I have read somewhere that, to ##\hat{U}## represent a symmetrie, it's necessary that ##\hat{U}^{\dagger} \hat{H} \hat{U} =...