Quantum states Definition and 86 Threads

Hi Everyone. I hope someone can point me in right direction. I am struggling to work this out . If it was 1d confinement the calculated n number would be the energy level. So for example n= 3, means that quantum number is n= 3 and there is 3 possible quantum states. Is that correct? With 3D box...

Hi, as discussed in this recent thread, for a particle without spin the quantum state of the particle is described by a "point" in the Hilbert space of the (equivalence classes) of ##L^2## square-integrable functions ##|{\psi} \rangle## defined on ##\mathbb R^3##. The square-integrable...

Ballentine, in his Chapter 8.1, appears to give the attached recipe for *in principle* preparing an (almost) arbitrary (pure) state (of a particle with no internal degrees of freedom) by the method of "waiting for decay to the energy ground state". My questions are fourfold: 1) From (8.1), we...

This pop article popped up (isn't that what they do, by definition?) on my google news page. https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states It claims that a thought experiment shows that doing a double-slit experiment near a black hole event horizon can reveal...

What's the difference between a bra vector and ket vector in specifying spin states except for notational convenience when calculating probablility amplitudes? Are they equivalent?

I have some basic questions about mixed states and entanglement. 1. Do mixed states always imply that the states are entangled and vice versa? 2. Can mixed states ever be separable? 3. Does interference have anything to do with entanglement? In terms of Density Matrices, ρ = |ψ><ψ|: 4...

I was working on plotting fidelity with time for two quantum states. First I used discrete time( t= 0,1,2,3...etc) to plot my fidelity. I got constant fidelity as 1 with continuous value of time. Next I used discrete set of values ( t=0 °,30 °,60 °,90 °). Here I saw my fidelity decreases and...

I was teaching the basics of quantum states and was showing the students that an arbitrary state in a quantum two-level system could be written as ##|\psi\rangle = C_1 |+\rangle + C_2 |-\rangle = R_1 |+\rangle + R_2 e^{i \alpha} |-\rangle##, with {##C_i##} complex and {##R_i##} real. Then...

hi guys i have a question about the derivation of the density of states , after solving the Schrodinger equation in the 3d potential box and using the boundary conditions ... etc we came to the conclusion that the quantum state occupy a volume of ##\frac{\pi^{3}}{V_{T}}## in k space and to...

I'm trying to understand the detailed concept of why the density of states formula is accurate enough to calculate the number of quantum states of an energy level, including degeneracy, within a small energy interval of ##dE##. The discrete energie levels are calculated by $$E = \frac{h^2 \cdot...

Hi all, This question asks me to calculate the number of quantum states, as well as electrons per cm^3 of the crystal in the room temperature. The problem is I only dealt with a single element before without any calculation for 1cm^3 whatsoever. For example for a Silicon semiconductor, I can...

Hi all, I'm right now confused about this. As far as I know, when changing from a level to another, the change in l (subshell) can only be a difference of 1, and ##m_{l}## can be the same or a difference of 1. In this case, since the question wants me to state possible quantum states of...

I calculated the total area of phase space and divided it by the area of one cell i.e. h. n = (x_0*m*2*v)/h => n = (0.1 x 10^-10 x 9.1 x 10^-31 x 2 x 10^7)/6.626 x 10^-34 => n = 0.27 This answer doesn't match with any of the options. What did I do wrong? Edit: The question was printed...

Elementary question: Is there ever a case where the solutions for a wave equation turn out not to be a vector (in Hilbert space of infinite complex-valued dimensions, or a restriction to a subspace thereof) , but something else -- say, (higher-order) tensors or bivectors, or some such? My...

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...

Hello, I have some trouble understanding how to construct the matrix for the beam splitter (in a Mach-Zehnder interferometer). I started with deciding my input and output states for the photon. I then use Borns rule, which I have attached below: To get the following for the state space...

Hi! I'm struggling with the following question: Show that if n quantum states ρ1, ..., ρn are pairwise perfectly distinguishable, they are also jointly perfectly distinguishable. Perfect distinguishability means that there is a set of psd matrices \{E_{1}, ..., E_{n}\},\, \sum_{i} E_{i} =...

In my textbook, quantum states are infinite dimensional vectors. But I was watching a lecture on QM and the professor referred to ##|v> <u|## as itself being a quantum state. Also I saw online people saying the same thing. Are tensor products just things that tell you whether or not the two...

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...

See title.

Hello everyone, We come to the end of another semester and its presentation time. I have chosen to discuss how to prepare different quantum mechanical systems for various applications. So my question for you guys is, are there any interesting experimental techniques I should look into. I am...

If the number of possible values of L is n, and the number of possible values of m is 2*L-1, and there are 2 spin directions.. shouldn't the total number of states be 2*(number of possible L)*(Number of possible m)? But this gives 4n^2 - 2n. I am extremely confused. Thanks for your help!

What does it mean to say that a quantum state or wavefunction is constrained?

Hi, I am learning quantum entanglement. I am interested to create an up to date list of all known : - Photon Quantum States - Particle Quantum States - Classically entagled photon states I guess that there is an organization out there that already have this info. If someone can point me into...

Hello everyone, My understanding is that a two-quantum state system is simply a system that can only be in two states. That is equivalent to say that the observable of interest that is being considered can only have possible values. Is that the case? If so, a classical bit can have two values...

I was just reading a paper <predatory publisher reference deleted> There is an argument (originally by Spekkens), in Section 2.1, that is supposed to be against psi-ontic interpretations. As I understand it, it's that if someone hands you a particle in state x+ or y+ you cannot tell the...

Here is an interesting article off of phys.org that I really liked. http://phys.org/news/2012-08-caught-camera-quantum-mechanics-action.html What I found interesting is its premise of visually capturing multiple quantum states so that one could personally inspect a lot of these issues that...

Homework Statement I apologize, this is not really a homework problem. I have an exam coming up, and I need to be able to explain the difference between a stationary/non-stationary quantum state in a qualitative way, and in what cases these states have time dependent probabilities. I am hoping...

Hi, I recently saw a derivation that included: [1] #CS = V_spatial * V_momentum [2] #QS = #CS/h (where # indicates it's the total number of the variable) quantum states = QS; classical states = CS; h is Planck's constant If possible, do you mind explaining or directing me to references...

Homework Statement Hey, the no-cloning theorem states, that arbitrary quantum states cannot be cloned by any circuit. It is, however, possible to clone orthogonal states. What would a circuit performing this action look like? Homework Equations Relevant equations: I am assuming you all now...

The quantum states ##\psi(x)## of the infinite square well of width ##a## are given by ##\psi(x) = \sqrt{\frac{2}{a}}\sin\Big(\frac{n \pi x}{a}\Big),\ n= 1,2,3, \dots## Now, I understand ##n \neq 0##, as otherwise ##\psi(x)## is non-normalisable. But, can't we get additional states for...

I have to find a unitary transformation that takes me from one quantum state to another (or if there is such a transformation), given the two quantum states in matrix form. The matrices are huge (smallest is 16x16) , so doing it on paper is not an option. Does anyone know how I can do this in...

Hey all, I'm reading through an anecdotal work about the philosophical foundations of quantum field theory and the authors keep referring to states having the ability to be "sharp." As in it's possible for P to be sharp if the system is mixed, where P is some property of the system. Thanks! IR

Max Tegmark in his paper “Many worlds in context” http://arxiv.org/abs/0905.2182 Argues that …. .“Everett’s MWI is simply standard QM with the collapse postulate removed, so that the Schrödinger equation holds without exception”. He also argues that from this we can deduce that not only...

Homework Statement A quantum-mechanical harmonic oscillator with frequency ω has Hamiltonian eigenstates |n with eigenvalues En = (n + 1/2) ħω. Initially, the oscillator is in the state (|0> + |1>)/√2. Write down how the state of the oscillator evolves as a function of time t. Calculate the...

Here is a thought experiment. Imagine Schrodinger's cat... in the traditional model, there is a single observer outside the box, and the observer creates an entanglement with the catbox device which reveals the quantum superposition of the enclosed cat. The cat is said to be in a superposition...

Are all quantum states represented by normal vectors?

Hello everyone. Can someone explains me the meaning of quantum state transition? For example consider an electron which is in the superposition of two energy eigenstates of a given hamiltonian, now, if no one perturbs the state with a measure, nothing happens and the superposition remains the...

Okay, here goes... Our teacher set a question in the last test which asked us to show that if a system initially be in a stationary state, it will remain in a stationary state even if the system evolves according to the time dependent Schrodinger equation. What I did was show that the...

I am a little confused about exercise 1.2 in the book "Quantum Computation And Quantum Information" By Michael Nielson. The question is: Explain how a device which, upon input of one of two non-orthogonal quantum states |a> or |b> correctly identified the state, could be used to build a device...

Homework Statement A particle is moving in one dimension, estimate the number of quantum states available to that particle if it is an electron confined in a region 10-9m long with speed less than 107 m/s (less than meaning velocity is between 107 and -107 m/s) Homework Equations...

Hello Forum, When a system is in a particular state, indicated by a |A>, we can use any basis of eigenvectors to represent it. Every operator that represents an observable has a set of eigenstates. I bet there are operators with only one eigenstate or no eigenstates. There are operators, like...

Hi guys, Sorry if this isn't quite the right place to post this, but I have a few conceptual questions that I'd like to clear up about time evolution of a quantum state. Firstly, what is the exact argument for the evolution operator \hat{U}\left(t,t_{0}\right) being independent of the initial...

I am watching James Binney's QM lectures on iTunes University, and also going through his free textbook. He is a tough teacher, but I love how many misconceptions he points out, and some of the points he makes are very subtle and mind blowing when the lightbulb comes on. I am confused on...

I am a retired electrical engineer, now able to get back to studying what I really enjoy - mathematics and physics. As a genuine old geezer, my modern physics knowledge, which was never very deep, is now way out of date. I purchased a copy of "Modern Physics", by Kenneth Krane, and have been...

Is it not possible to deduce quantum states from a density matrix?

In any textbooks I have seen, vacuum states are defined as: a |0>= 0 What is the difference between |0> and 0? Again, what happens when a+ act on |0> and 0? and Number Operator a+a act on |0> and 0?

Consider the Gaussian Integral (eqn 2.64).. is anyone able to explain how the constant of normalization is rationalised?

Are systems ever in a pure quantum mechanical state? If they are, is it possible to know the precise pure QM state? The example I am thinking of is the spin of an electron. If we measure the spin about the "z-axis" and find the result to be "up" then we say the electron is in the pure state...

When we speak about wave function of an electron, we write it as ψ_{n,σ} (x,ζ) so that we specify here the orbital quantum number by n and spin quantum number by σ. σ can take two values according to spin up or down. x is space position and ζ has two discrete values related to spin up and down...