States Definition and 1000 Threads

Hi, I'm currently working on showing the relation of quantum fidelity: The quantum “fidelity” between two pure states ρ1 = |ψ1⟩⟨ψ1| and ρ2 = |ψ2⟩⟨ψ2| is given by |⟨ψ1|ψ2⟩|^2. Show that this quantity may be written as Tr(ρ1ρ2). I've been following the wikipedia page on fidelity but can't...

Most of the books I've seen they say that the first excited state of Helium (with two electrons, one in orbital 1s and other in 2s) can have the two electrons with parallel spin (orthohelium) or anti-parallel spin (parahelium). If ##\operatorname{X_{↑}}{\left (n \right )}## represent the state...

I'm reading the following paper. https://arxiv.org/abs/1409.1570 Is there an epistemic model of a qubit in which the number of ontic states is finite? I realize Spekkens toy bit discussed in the paper has only 4 ontic states, but it seems to only model a qubit that was prepared in one of 3...

EDIT: Questions have been revised below, those immediately following are for reference, jambaugh's kind reply was in direct response to these original questions. Could a completely unitary (QM) process act on a set of particles in "completely identical quantum states" to cause them to time...

Hi My question relates to existence of metastable states in atoms which help out laser production. Is there any physical reason why some orbits allow electrons to stay for comparatively longer time 10-3 s than others which allow only 10-8s? Is this stay time same for all materials? Please guide.

Hi, I'm an undergrad, following my very first serious course in QM. We're following Griffith's book, and so far we're staying close to the text in terms of course structure. Griffiths starts out his book by postulating that each and every state for any system \Psi must be a solution to the...

Suppose a set of basis vectors are eigenvectors of some operator. So they will provide a one dimensional representation of that operator in the vector space?

Could I have hundred times the ground state or there is a limit? Is there a limit for excited magnetic momentum that if reached the nucleous explode or generate gammas? I suppose If I excite it it would spin faster but proportional to quantum values. Note: there is a "theory" to avoid electron...

A question came up about deducing the number of possible energy states within a certain momentum ##p## using momentum space. To make my question easier to understand, I deliberately chose ##p## and not a particular increment ##dp## and I assume a 2 dimensional momentum space with coordinates...

I've been reading a bit about the quantum confinement effect on nanowires, particularly how it changes the band structure. I'm trying to find an explanation on why the density of states splits into sub-bands. At the moment all I'm running into is 'because of the quantum confinement effect' which...

In Wikipedia's outline of the Many Worlds Interpretation of quantum physics https://en.wikipedia.org/wiki/Many-worlds_interpretation, it states "In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence,...", yet I thought decoherence...

I'd like to see whether or not I understood correctly how massive particle states will transform under a homogeneous Lorentz transformation, in terms of the standard four-momentum ##k = (0,0,0,M)##. I suppose we can write $$U(\Lambda) \Psi \propto D^{(j)} (W(\Lambda)) \Psi$$ where ##U(\Lambda)##...

The MB energy distribution is: MB_PDF(E, T) = 2*sqrt(E/pi) * 1/(kB*T)^(3/2) * e^(-E/(kB*T)) How do I arrive at the density of states which hides inside the expression 2*sqrt(E/pi) * 1/(kB*T)^(3/2) ? I've only seen DOS that have "h" in them.. I want it to contain only E, pi, kB and T.. This is...

Do simple 2D Ising models have constant density of states? How is it calculated?

Homework Statement Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle## Homework Equations...

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you don't see image here is the matrix which is 2X2 in MATLAB code: [9/25 12/25; 12/25 16/25] Homework...

Moderator's note: This is a sub-thread spun off from https://www.physicsforums.com/threads/is-the-ground-state-energy-of-a-quantum-field-actually-zero.953766/. I should have said that in certain cases in QFT, we can neglect “surface terms”. For example, the (on-shell) difference between the...

Hi, I'm dealing with the following problem. I hope someone could help me with it. Problem is about 2 interacting particles (spin: 1/2 each), with Hamiltonian Ho=-A( S_1z + S_2z) and perturbation H1={(S_1x)*(S_2x) - (S_1y)*(S_2y)}. The question asks to calculate the energies of all 4 states up...

Hi, I just started a book on QFT and one of the first things that was done was switch from labeling states with their individual particles and instead label states by the number of particles in each momentum eigenstate. In addition, some "algebras" (not sure if they qualify by the mathematical...

The BE-distribution for the case of only one state per energy level (gi = 1) is ni = 1 / (exp(ui - μ)β - 1) This is a reasonable and well defined distribution as far as I can see. On the other hand the number of possibilities to realize a given distribution of bosons among k energy levels with...

I'm watching a lecture and the professor is talking about generic quantum states as |\psi> He's making the point that this state is very generic. It can represent anything. He references some examples like the polarization of a photon and the path of a photon and the spin of an electron...

We have a 1 dimensional infinite well (from x=0 to x=L) and the time dependent solution to the wavefunction is the product of the energy eigenstate multiplied by the complex exponential: \Psi_n(x, t) = \sqrt{\frac{2}{L}} \sin(\frac{n\pi x}{L}) e^{-\frac{iE_n}{\hbar}} Now, I want to create a...

I am trying to understand how to think about a state of the form: |\psi \rangle=\alpha|H_A H_B\rangle+\beta|V_A V_B\rangle where |\alpha|\neq |\beta| It is between pure entangled state and a classical state like \psi \rangle=|H_A H_B\rangle, but it is not mixture of the two either. So it seems...

Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with...

I'm watching a lecture on the intro to quantum computing. See the attached image which will be useful as I describe my question. So the professor says that we have this single photon and it's in this state, ## | 0 > ##. He states that when we send this photon through a beam splitter that it...

I have a question (more like a curiosity) related to three-dimensional topological insulators, which support Dirac-like states at their surfaces. From the theory, it is well known that these states are immune to scattering from non-magnetic impurities, i.e. impurities that do not break...

I read this wiki and some of the references https://en.wikipedia.org/wiki/Bound_state But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim. Thanks

I am studying Quantum Cryptography and I am quite new in Quantum area. I have read an article and I found this confusing statement: My questions: 1. The three stage protocol implementing multiphoton. What is the meaning of coherent states of mean photon number? 2. How to describe the quantum...

Am I understanding it correctly that if you keep acting with an internal 2-dimensional creation operator on a string you will get heavier and heavier particle from the 11-dimensional (26 dimensional) point of view? If so, how come we haven't observed those particles in the real life? Is it...

I'm to get the density of states of 1-dim linear phonons, with N atoms. I think it's a lot similar to that of 1-dim electrons, except that two electrons are allowed to be in one state by Pauli exclusion principle. To elaborate, ##dN=\frac{dk}{\frac{2π}{a}}=\frac{a}{2π}dk## for...

Can anyone with basic knowledge of Dicke States assist with explaining how we arrive at equation (4) in the paper 'Entanglement detection in the vicinity of arbitrary Dicke states': <Moderator's note: link fixed> $$\langle J^2_{x} \rangle_{\mu} = \sum_{i_1,i_2} \langle J_{xi_{_1}} \rangle_{\mu}...

Hello! The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows: ##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##. How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant? Thanks in advance!

Hello! I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of...

Homework Statement Using the heats of fusion and vaporization for water, calculate the change in enthalpy for the sublimation of water: H2O(s) --> H2O(g Using the delta H value given in Exercise 24 and the number of hydrogen bonds formed to each water molecule, estimate what portion of the...

This thread refers to a paper I am working on. The paper said in the model section that: In the complete set of scattering states we distinguish two orthogonal set of eigenfunctions: (i) the states − → ϕ incoming from the left, and (ii) the states ←− ϕ incoming from the right. Away from...

Is the equation used to determine the density of interface states in schottky diodes from capacitance- frequency data applicable to PIN junctions?

In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##. Given the state ##\omega## we can consider the GNS construction...

Homework Statement A bound particle is in a superposition state: \psi(x)=a[\varphi_1(x)e^{-i\omega_1t}+\varphi_2(x)e^{-i\omega_2t}] Calculate <x> and show that the position oscillates. Homework Equations <x>=\int_{-\infty}^{\infty} \psi(x) x \psi^*(x) \mathrm{d}x The Attempt at a...

What is the energy gap between the ground state (n=0) and the first excited state (n=1) of an electron trapped in a deep rectangular potential well of width 1Å?

I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help. My doubt ELI5...

Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables. Here we have the algebraic states. These are defined as linear functionals...

Hello Forum, Just checking my correct understanding of the following fundamental concepts: Stationary states: these are states represented by wavefunctions ##\Psi(x,y,z,t)## whose probability density function ##|\Psi(x,y,z,t)|^2 = |\Psi(x,y,z)|^2##, that is, the pdf is only a function of space...

A pure state can be interpreted as belonging to a system, but it can also be interpreted as belonging to a single particle (although the resulting probability is in respect to the system), and as I understand it, this is now the preferred interpretation. But in...

From Weinberg's Quantum Theory of Fields vol 1. In Chapter 2.5, he lists the transformation rule of a one-particle state under a homogeneous Lorentz transformation: \begin{equation} U(\Lambda)\Psi_{p,\sigma} = \sum_{\sigma'}C_{\sigma'\sigma}(\Lambda,p)\Psi_{{\Lambda}p,\sigma'} \end{equation}...

I am studying about the cavity radiation inside a metallic cube. In the textbook it states that there are two independent waves corresponding to the two possible states of polarization of electromagnetic waves. What does it mean by this? (My current assumption is the phase change of the waves)...

My textbook in elementary Q.M. stated that orbital electrons in an atom must have stationary state wavefunctions. Was this just a simplification, the truth being maybe that their wavefunctions can be nonstationary for a little while, but soon decay into stationary ones? I’ve seen an answer...

How can we differentiate among the lifetimes of the excited states of the hydrogen atom? The states are: 2p, 2s, 3s, 3p

Hello everybody. I am trying to understand better what happens at a liquid-gas phase transition for the Van Der Waals model. From what I have understood, from the Van Der Waals model we are able to plot the curve P(V) and to calculate the free energy F. Here are such curves : Then, we...

[Mentor note: Thread title changed to describe actual problem being presented] 1. Homework Statement Homework Equations The Attempt at a Solution I understand you have to interpolate temperature and pressure of the saturated vapor from the table, since there is no matched final specific...

Homework Statement Part C) Please: Homework Equations above,below The Attempt at a Solution so I think I understand the background of these expressions well enough, very briefly, changing the manifold from ## R^n ## to a cylindrical one- ##R^{(n-1)}^{+1}## we need to cater for winding...