States Definition and 1000 Threads

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...

Homework Statement Attached: Homework Equations Euler-Lagrange equations to find the EoM The Attempt at a Solution [/B] Solution attached: I follow, up to where the sum over ##\mu## reduces to sum over ##\mu=i## only, why are there no ##\mu=0## terms? I don't understand at all. Many...

Hi. Does someone that know more about US economy can help me in answering this question? Which are the most profitable sectors in the USA that create a so high GDP? The manufactural one ? For example my country ( Italy) have a great tourism sector, almost in every periodo f the year people...

Consider the QM postulate which states that physical states are represented by rays in a Hilbert space. Consider a ray ##R##. An observer from other frame will have a correspoding ##R'## which can be either - equal to ##R## or, - not equal to ##R## Suppose the two frames are inertial frames...

Scientists are exploring new states of light with orbital angular momentum https://futurism.com/harvard-scientists-made-material-creates-completely-new-states-light/ Research paper http://science.sciencemag.org/content/early/2017/11/01/science.aao5392

Hello PF! I was reading https://en.wikipedia.org/wiki/Fubini–Study_metric (qm section like always :wink:) And can't figure out how to derive: \gamma (\psi , \phi) = arccos \sqrt{\frac{<\psi|\phi><\phi|\psi>}{<\psi|\psi><\phi|\phi>}} I started with \gamma (\psi , \phi) =|| |\psi> - |\phi>||=...

Hi. I just want to check that I understand the following. If I have a general superposition of wavefunctions satisfying the TDSE then that superposition also satisfies the TDSE. But that superposition only satisfies the TISE if the energies are degenerate because the TISE is an eigenvalue...

Homework Statement 1D atomic chain with one atom in the primitive cell and the lattice constant a. The system in described within the tight binding model and contains N-->∞ primitive cells indexed by the integer n. The electronic Hamiltonian is $$H_{0} = \sum_{n} (|n \rangle E_{at} \langle n |...

Homework Statement I have the following definition of the space-time coordinates Homework Equations Working in a certain gauge we can also do: From which we can find: Where ##N_{lc} ## sums over the transverse oscillation modes only. The Attempt at a Solution [/B] MY QUESTION: I...

Before I begin, I would like to say what I am about to ask would require some sort of top-top-bottom bound state for it to function. Which (to my knowledge) has not been experimentally or theoretically predicted. Also, in case if you are wondering- no, this is not a homework question. --- So...

Edit: I'm pretty sure I have answered my own question. I think I need to sandwich the integral between a bra and ket to pick out one term from the sum. 1. Homework Statement Show that a Fock state ##|n\rangle## can be represented by the integral $$|n\rangle = \frac{\sqrt{n!}}{2 \pi r^n}...

In general, is it of more interest to consider multi particle states consisting of fermions & bosons or multi particle states consisting of only fermions (or only bosons)? I have seen that if it's of the latter type, then the study becomes in certain way more easy to carry on, though the former...

Homework Statement A state of a system of many noninteracting particles can be specified by listing which particle is in which of the accessible single particle states. In each microscopic state we can identify the number of particles in a given single particle state ##k##. This number is...

Can the kind members of this forum please help me make the logical leap from an entangled pair of electrons or photons to that of the pair being in a superposition where the observation of one effects the state of the other? For example, my understanding is that, through the conservation of...

I was reading the *Statistical Physics An Introductory Course* by Daniel J.Amit and need some help to understand a certain passage: In an isolated composite system of two paramagnetic system: System a with ##N_a## spins and a magnetic field ##H_a ## System b with ##N_b## spins and a...

Hi all - forgive me, I'd asked a series of questions in a previous post that was deemed to be circular, but I still didn't obtain a satisfactory answer to the question I was asking. In this post, I'm going to try to be very careful to use terms that are at least less 'misplaced', per se...

I've read Arnold Neumaier's excellent Insight article on virtual particles, but I'm very confused about one thing: Observable particles are considered to be on-shell, and as 'asymptotic states' at time +- infinity. Now, in a scattering experiment, I may produce a new particle, which will travel...

Since proper time for photons doesn't change, i.e. in their reference frame time doesn't change, then it should be that photons don't change their quantum mechanical state, or the equivalent in Maxwell's theory. One could say, well they don't experience time, but we do. Okay, but since their...

Upon reading Landau QM, the Principle of superposition of states, I got confused. It states (and i quote): "Suppose that, in a state with wave function Ψ1(q), some measurement leads with certainty to a definite result 1, while in a state with Ψ2(q) it leads to a different result 2. Then it is...

Hi. 1. Does a pure state belong to mixed states \hat{\rho}=\sum_k p_k|\psi_k><\psi_k| where ##p_k=1## for k=i and otherwise 0 ? 2. Does quantum jump by observation work for both mixed and pure states ? Your teachings will be appreciated.

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Hello! I am reading some representation theory/Lie algebra stuff and at a point the author says "the states of the adjoint representation correspond to generators". I am not sure I understand this. I thought that the states of a representation are the vectors in the vector space on which the...

Hey am new to this forum but I have a question regarding topologically protected states.. Let's suppose we have a 1D gapped system divided two to distinct regions that have different periodicity or different properties and that at the centre, where the two regions 'meet' states appear in the...

According to decoherance. Say there is a pure state initially in state: |ψ⟩=α|0⟩+β|1⟩ After decoherance (interaction with environment), the system will transform into the improper mixed state of: ρ=|α|2|0⟩⟨0|+|β|2|1⟩⟨1| This is the "apparent" collapse that decoherance refers to. With the...

Hey guys, I am having issues with understanding the physical nature of pure and mixed states. Maybe you can help me out? 1) A pure state - superposition is a state that consists of different states at the same time. It's like having several waves, each one belonging to an Eigenstate of the...

Hello, Let's suppose we have a two dimensional lattice which is periodic along certain direction, say x-direction, allowing us to define a quasi momentum k_x. The lattice is not periodic along the y-direction (perpendicular to x-direction). Therefore, we are able to obtain the band structure...

What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...

why are energies of the stationary states negative ??

Homework Statement Show that to a first approximation the equation of state of a gas that dimerizes to a small extent is given by, ##\dfrac{PV}{RT} = 1 - \dfrac{K_c}{V}## Where ##K_c## is equilibrium constant for ##A + A \iff A_2## Homework EquationsThe Attempt at a Solution Using virial...

Homework Statement Homework EquationsThe Attempt at a Solution In (b), if particle B has up spin (x-axis), then A should have down-spin(x-axis). The problem ask the state by using lma,mb> state. This state is valid only in z-axis, but how can i represent that state ?? I think the answer is...

Homework Statement Hi everybody! In my quantum mechanics introductory course we were given an exercise about the 3D quantum harmonic oscillator. We are supposed to write the state ##l=2##, ##m=2## with energy ##E=\frac{7}{2}\hbar \omega## as a linear combination of Cartesian states...

Hi, How can I give a good summary about the main and real difference between these three states? physically and mathematically. Thanks

Putting a soft photon in vacuum will result in a zero energy vacuum state. Despite the zero energy, has this state vacuum fluctuations? Putting more of these photons will result in more vacuum states. Would they have vacuum fluctuations as well resulting in more vacuum flctuations? A total...

Hey there, With covalent bonds, we have bonding and antibonding states. If we now have, let's say sp or sp2 states, doesn't matter, is there an equivalent bonding or antibonding state related to this sp bond ? I mean, why sp states wouldn't have antibonding states like every normal covalent bond ?

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...

Suppose we have a classical particle in box. The number of degrees of freedom is 6. The position of the particle and its momenta. Now if we want to calculate the entropy of the system as a function of the energy we only need to find a relation between all the possible states the particle can be...

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!

The way I am coming to understand it, the allowed states that an observable can be "observed/measured" in are defined by the eigenvectors (and associated eigenvalues) of the observable's operator. Since those eigenvectors form a basis and span the space of vectors defined by the operator, a...