States Definition and 1000 Threads

Can a state only be formulated with respect to an observable in consideration? That is to say, does the formulation of the state depend on the particular observable in consideration? Thanks.

I got (very) confused about the concept of states, pure states and mixed states. Is it correct that a linear combination of pure states is another pure state? Can pure (and mixed) states only be expressed in density matrices? Is a pure state expressed in a single density matrix, whereas mixed...

I'm having trouble with the mathematics of tensor products as applied to Bell states. Say I have the state \begin{align*} \left|\psi\right> &= \frac{1}{\sqrt{2}} \left(\left|0\right>_A \otimes \left|0\right>_B + \left|1\right>_A \otimes \left|1\right>_B\right) \end{align*} How would the...

Why is the triplet state space wave function ΨT1=[1σ*(r1)1σ(r2)-1σ(r1)1σ*(r2)] (ie. subtractive)? How does it relate to its antisymmetric nature? Also, why is this opposite for the spin wave function α(1)β(2)+β(1)α(2) (ie. additive)? And why is this one symmetric even though it describes the...

Homework Statement I'm going back through some homework as revision, and came across this problem. It was marked as correct, but now I'm thinking it's unconvincing... For a particle in an infinite square well, with ##V = 0 , 0 \leq x \leq L##, prove that the stationary eigenstates are...

Hi all! Sorry if this question is stupid. The the time-independent schrodinger equation describes energy for a time-independent system, and the time-dependent schrodinger equation describes the time evolution of the wavefunction. So, how would you describe the energy for a time-dependent system...

The first spin analyser is orientated on the z-axis and the second is in a arbitrary N-direction. My thought process I can't get past is below If I find particle 1 to have spin up in Z-direction, the state collapses and the second must be spin down in the Z-direction for the particle at the...

The triplet spin state with a normalisation constant of 1/√2 and the singlet spin state with the same normalisation constant... Where on Earth is this normalisation constant derived from? I've been scouring the Griffiths intro to quantum mechanics textbook and can't find info on it.

Is the solution of the time-independent schrodinger equation always a stationary state? Can it be non-stationary?

Spin up and spin down states in the x direction can be written as |Upx> = 1/ √2 ( |Upz> + |Downz> ) and |Downx> = 1/ √2 ( - |Upz> + |Downz> ) My textbook just stated the above facts without referencing why and I've been going through the spin chapter for a while now and I can't see it. Why...

Hi all, I have a question about Slater Determinant for excited states. Let's say we want to construct approximate (2 level) wavefunction of He in some certain state. Since we have two electrons in two level system with spin in consideration, we can construct total of 4 different wavefunctions...

Im having trouble with my thought process for spin states of a system of two electrons Using Total Spin 'S' and Total spin mag quantum numbers 'MS' as state ket |S MS> My textbook states... " Three Symmetric Spin states Triplet spin stats for twin identical spin -1/2 particles | Up Up> = |S...

Homework Statement I am trying to calculate the ratio of the density of states factor, ##\rho(p)##, for the two decays: $$\pi^+\rightarrow e^++\nu_e~~$$ and $$\pi^+\rightarrow \mu^++\nu_{\mu}~~$$ Homework Equations ##\rho(p)~dp=\frac{V}{(2\pi\hbar)^3}p^2~dp~d\Omega## Which is the number...

I am not sure exactly what E = mc^2 means. 1. Does it simply means if we were able to convert mass into energy this is the amount of energy. 2. That mass and energy are different states of the same thing. An example would be water which can either be a solid (ice), a liquid (water) or a...

Homework Statement The problem is given above. I am struggling on the first two parts, where I am tasked with finding gamma and beta. Homework Equations For spin one half states in arbitrary directions, I know that psi = a*|n;+> + b*|n;-> . |n;+> = cos(theta/2)|+> +sin(theta/2)*ei*phi|->...

I know that if I multiply e^3/2 (e= 1.602x10^-19) to the unit below I can change it to eV Can somebody help me I don't know why

I have googled it and cannot find anything. Apparently the rule that transition metals want full or half-full orbitals is false. I understand why the 4s orbital would be lost but I don't understand why some d electrons would be lost. For example in Mn6+, the electron configuration would be [Ar]...

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...

I'm reading through some lecture notes for QM in a subsection about stationary states where the definition of orthonormality involving a kronecker delta \int_{-\infty}^{\infty}\psi_n(x) \ \psi_m^*(x)dx=\delta_{m,n}and the formula for some wavefunction that is a superposition of energy...

Hi, I am about to work on the problem of trying to find a renormalization program for bound states in QFT. Any suggestions/advice on where to start would be much appreciated.

If I try to send a vertically polarized photon through one slit and a horizontally polarized photon through the other slit, they actually go through both slits. But when I measure and find out through which slit the horizontally polarized photon went, I automatically know that the vertically...

I think this is just a quickie. I'm interested in what is assumed about entangled photons/particles before they are observed. Is it correct to assume that the photons/particles exist in all possible states simultaneously? Thank you.

It is easy to show that when you have a quantum system, let's think for example in electrons in a metal, then there appears summation over electron states of the form, e.g. for the energy for a free electron gas at T=0K: ##E=2 \sum_{k\leq k_f} \frac{\hbar^2}{2m}k^2## Where ##k_f## denotes the...

Hello, I am new to the forum, so I am directly stating my questions. 1)What determines the density of states of Phonons in a semiconductor? 2)Does degeneracy of semiconductors depend only on doping? Thanks

If you raise the electron to other higher shell states, can light transmission throug -h a SOLID BLACK opaque object. Modified the original question because it was unclear. I won't repeat the same question over, and over, but what I have said in previous questions may get repeated in the...

On Wikipedia, an article appear from which I quoted below. Here is something called Bose-Einstein correlation due to interference of wave character that I confuse with quantum entanglement. I want to know if these BEC correlations are entangled or separable states...

Homework Statement Hello all, Im asked to construct the state | \frac{5}{2} , \frac{3}{2} \rangle from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle . Homework Equations Clebsch Gordon Coefficient's table The Attempt at a...

The following is taken from page 13 of Peskin and Schroeder. Any relativistic process cannot be assumed to be explained in terms of a single particle, since ##E=mc^{2}## allows for the creation of particle-antiparticle pairs. Even when there is not enough energy for pair creation, multiparticle...

I am wondering if my understanding of superposition concept is correct. Forgive me for not using QM braket notation, I am new on this site and don't know how to embed it in the post. What confuses me about superposition concept is that people often say that some system can be in two (or more)...

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...

Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature. In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}## ##...

Hi there people! So my question is why you can see localized surface states within the band gap of the material with an STM. How is a tunneling circuit being established?

An example of a two-qubit state is one of the Bell states, for example: lB> = 1/√2 (l00> + l11>) In my book it is stated that the Bell states form an orthonormal basis for the set of two qubit states. But what exactly is the general form of a two-qubit state? Is it any vector of the form: lq>...

From the Ehrenfest theorem, we know that the equation below is correct for any state ## \psi ##. ##m\frac{d^2}{dt^2}\langle x \rangle_{\psi} =-\langle \frac{\partial V(x)}{\partial x} \rangle_{\psi} ## But then one of the definitions of coherent states is states for which the expected value of...

I'm Canadian and looking into quite a few different graduate programs in Physics. I am still quite open to different opportunities, and have found some interesting Master's programs (both MSc and MASc) here that are funded. But outside of Canada, I was looking into applying for graduate programs...

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we...

Fermi's golden rule contains a term that is the density of the final states ##\rho(E_{final})##. For my problem we have no time depending potentials so that's the same as ##\rho(E_{initial})##. If I understand the definition of ##\rho## correctly, it's the number of states in an interval...

I Have a question about how we arrive at the probabilities for the wavefunction collapsing to some specific value for an observable. As far as I'm aware, the wavefunction is a superposition of possible states depending on the observable we try to measure. Lets say I want to measure observable...

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...

Guys I have a doubt When we calculate the trial function We do it for the wave function of the orbitals Right in order to get the total orbital energy (Which included the energy of the electron) and that of the orbital Well my question Is does the orbital possess Some energy even if the electron...

Hello I am confused and I can't figure out what is meant by phase when it comes to quantum mechanics for single photons and coherent states as I am a new to this field. Best regards

I am looking over my notes for quantum mechanics, particularly for electronic state classification for nitrogen. At ground state, nitrogen atom's 1s and 2s shells are fully filled and the 2p shell is half filled, thus the configuration is: ##2s^2 2p^3## There are 3 different angular momentum...

Homework Statement Given a orthonormal basis of the hilbert space of qutrit states: H = span (|0>, |1>, |2>) write in abstract notation and also a chosen consistent matrix representation, the states a) An equiprobable quantum superposition of the three elements of the basis b) An...

Homework Statement Construct the decompositions ##\mathbf 2 \otimes \mathbf 2 = \mathbf 3 \oplus \mathbf 1##, where ##\mathbf N## is the representation of su(2) with ##\mathbf N## states and thus spin j=1/2 (N-1). Homework Equations Substates within a state labelled by j can take on values -j...

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...

Hi All Thanks for welcoming me to the physics forum. I am reading Greiner and Mueller's Quantum Mechanics: Symmetries and am stuck at not understanding the vector meson ( rho meson)'s spin states. For S=1 we get three states -1, 0, and 1. Prof. Mueller separated them as a rho +/-1, and rho 0 ...

Hi, if there was a big bang I would assume a countable number of states, if the universe is build of quantum portions in time and space? Thanks!

Homework Statement I figured out 4a, but I'm just struggling a bit with 4b. Homework Equations Relevant websites highlighted above (respectively): http://www.nist.gov/pml/data/handbook/index2.cfm http://physics.nist.gov/PhysRefData/ASD/lines_form.html The Attempt at a Solution This is...

Why mesons mixed states are defined as SOMETHING +/- SOMETHING [+/- SOMETHING] normalized by 1/sqrt(2) or 1/sqrt(3), So the sum uses quotient +1 or -1. But in electroweak symmetry breaking charged W boson is defined as W1 (+/-) i*W2, so the quotient is +i or -i. So why mesons never use...