States Definition and 1000 Threads

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...

I have a state |0>|alpha>. Now I want to evolve this state at any time t and find the fidelity between the initial and final states. Any ideas how to do that? My main problem is that I don't know how to evolve this state.

Hi everyone! I've been studying quantum mechanics for a while but I have a big big problem. If a system is in an eigenstate of energy (I use the eigenstate as a basis) it remains in this state forever. But if I describe the system with a different set of basis states (not eigenstates) the...

The coherent state can be written in terms of e^(αb†+α∗b)|0>. But how the even coherent state i.e. |α>+|-α> can be written in terms of displacement operator?

Hello! Are there any experimental measurements or theoretical calculations of the electric dipole moment of any Rydberg state for CaF or BaF? Thank you!

I saw on Wikipedia that Fe has both positive and negative oxidation states. I know that Fe will willingly give up its 2 electrons to form an ionic bond with O for example, making it Fe+2. 1. But how can Fe+3 exist? This means it gives up three electrons right? Does this mean the Fe atoms...

It's probably more kind of math question. I consider a wave function of a harmonic oscillator, i.e. a particle in a parabolic well of potential. We know that the Hamiltonian is a Hermitian operator, and so its eigenstates constitute a full basis in the Hilbert space of the wave function states...

hi guys i came across this question about the maximum and minimum number of bound states that can be confined in these potential wells 1- infinite potential well 2- semi infinite potential well (from one side) 3 - finite potential well i think i have a good idea about the minimum number of...

Hello! Assuming we have a 2 level system interacting with an EM field in the RWA and dipole approximation, we would have in the basis of the 2 unperturbed atomic states a 2x2 Hamiltonian matrix with off-diagonal terms. By diagonalizing this Hamiltonian we obtain dressed states which are the...

I've attached pictures with the circuit and part of the attempted solution. I've replaced the diode with its offset model and obtained the equivalent circuit in the 2nd picture. After applying KVL, I've obtained that u_l=−u_D−i_D*R. Since U_D0 is greater than 0, I've deduced that the diode must...

I'm an undergrad in physics, and have been asking myself the following question recently. Suppose you have a pure quantum state p (von neumann entropy=0), made of 2 sub-states p1 and p2 that are entangled. Because they are entangled, p \neq p1 x p2. Hence the entanglement entropy of p (=0) is...

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I am confused here. For ##x>0## particle is free and for ##x<0## particle is free. That I am not sure how we can have bond states. If particle is in the area ##x>0## why it feel ##\delta## - potential at ##x=0##. Besides that, I know how to solve problem. But I am confused about this. If we...

Hello! I am reading about dressed states, and I am presented a situation in which we have a laser (the pump laser) on resonance with a 2 level (atomic) transition, and a second, weak laser (probe laser) that is scanned over a frequency range. The absorption spectrum of the probe laser, for...

I have a question from the youtube lecture That part starts after 42 minutes and 47 seconds. Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.

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...

When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the...

Hello! Assume we have a 2 level system, with the ground state defined as the zero energy level and the excited state having an energy of ##\omega_0##. If we apply an oscillating electric field (assume dipole approximation and rotating wave approximation) of frequency ##\omega##, we have a time...

Suppose that we have two atoms with one proton one electron each, and these electrons interact with each other. The states for the electrons are the singlet(S=0) and the triplet states(S=1). My question is if i have to keep the nuclear spin of the protons parallel when i write the states, for...

How do you prove Heisenberg uncertainty relations for mixed states (density matrix), only from knowing the relation is true for pure states?

The equation $$\frac{\hbar^2}{2m}\frac{d^2u}{dr^2}-\frac{Ze^2}{r}u=Eu$$ gives the schrodinger equation for the spherically symmetric functions ##u=r\psi## for a hydrogen-like atom. In this equation, substitute an assumed solution of the form ##u(r)=(Ar+Br^2)e^{-br}## and hence find the values...

Consider page 2 of Toth's paper Entanglement detection in the stabilizer formalism (2005) . To detect entanglement close to GHZ states, they construct entanglement witnesses of the form $$\mathcal{W} := c_0 I - \tilde{S}_{k}^{(GHZ_N)} - \tilde{S}_{l}^{(GHZ_N)},$$ where...

I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##. Replacing ##p## by...

If the state considered is :##\frac{1}{\sqrt{2}}\left[\left(\begin{array}{c}1\\0\\0\end{array}\right)\left(\begin{array}{c}0\\1\end{array}\right)-\left(\begin{array}{c}1\\0 \end{array}\right)\left(\begin{array}{c}0\\0\\1\end{array}\right)\right]## It seems to me it were not locally measurable...

He told me I "need to show that the Hamiltonian matrix elements you get by using those states have nonzero elements only on the diagonal." I understand what and how a diagonal matrix works, but what I don't understand is what those states are. Are they states I put in my "quantum mechanical...

I observe that all bound states have discrete energy levels, eg. particle in a box, hydrogen atoms. But unbound states always have a continuous energy spectrum. For example, for the case of a finite potential well, when ##E<V_0##, we have discrete energy for the bound states. When ##E>V_0##, the...

Summary:: Comparing education systems from different countries. ..our education system is easier? Or does that mean our material is tougher and the grading system balances out? Or is just cultural differences. The only exception is York. It doesn't like (-) so an 80 is just an A. 90+ is an A+.

I see that this procedure helps to get rid of the two extra degrees of freedom (due to the scalar and longitudinal photons) one firstly encounters while writing the electromagnetic field theory in a Lorentz-covariant way; it indeed shows that modifying the allowed admixtures of longitudinal and...

Given the Bell State in Z basis ##\psi = (a\uparrow \downarrow - b\downarrow \uparrow )## where ##a^2+b^2=1##. Now Alice has one particle and sends the other to Bob. Suppose Alice decides to measure her particle in Z direction. Thus entanglement collapses. Query: 1. How do we know which...

Hi guys, I hope you all are doing great. If we take the double slit experiment for instance, before measurement particles are in a superposition of states. Once they are "measured", or non arbitrarily interfered with, their wave function collapses and only one state remains. So my question is...

I've got this question here, I know to calculate steady states you set dn/dT and dc/dT to 0 and then solve. However can anyone help me understand what it means by the "two cases" and how you go about this?

Anyone able to calculate the steady states?

Recently, I was giving a presentation for my research group related to ARPES to improve my understanding. I mentioned that the probing depth of ARPES is a few angstroms, meaning we can only look at surface states, and I was sort of giving a real space picture. In other words, ARPES can only...

Practically it is said that, given two spin states |u⟩ (up) and |d⟩ (down) - which are the spin measured along the +z and -z semiaxes - such that they are orthogonal ( ⟨u|d⟩ = ⟨d|u⟩ = 0), it is possible to write any other spin states using a linear combination of these two (because they are a...

This is what I have so far: $$ |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + \alpha^*\beta\Psi_1^*\Psi_2 + \alpha\beta^*\Psi_1\Psi_2^* $$ $$=> |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + 2Re(\alpha^*\beta\Psi_1^*\Psi_2) $$ I am...

I've tried to square and compare ##\Delta X## and ##\Delta P## but they are not equal I have to say I am pretty lost here and a hint would be appreciated. I have studied coherent states and I know how to proof some properties related to it. For instance, I see how to proof that the state is...

I have trouble understanding the solution to a homework problem. Consider the interaction Lagragian ##\mathcal{L}_{\rm int} = -iqA_\mu \bar{\psi}\gamma^\mu \psi##, i.e. photon-electron/positron interaction. We want to focus on the Compton scattering $$e^-(\vec p_1, \alpha) + \gamma(\vec p_2...

E = (1/√2)^2(E1) + (1/√2)^2(E2) = (E1+E2)/2 Let ψ(x,t=0) = ψ0 So, ψ1 = ψ0*exp(-i*E*T1/ħ) and, ψ2 = ψ0*exp(-i*E*T2/ħ) Given, <ψ1|ψ0> = <ψ2|ψ0> = 0 So, <ψ0*exp(-i*E*T1/ħ)|ψ0> = 0 => exp(i*E*T1/ħ)<ψ0|ψ0> = 0 => exp(i*E*T1/ħ) = 0 Similarly, exp(i*E*T2/ħ) = 0 So, exp(i*E*T1/ħ) = exp(i*E*T2/ħ)...

For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons). I am getting the 2D density of states formula as :- g(p)dp = 2πApdp/h^2 I think this is the formula for normal particles, and so for photons I need to...

According to the Many Minds interpretation of quantum mechanics (https://en.wikipedia.org/wiki/Many-minds_interpretation), the distinction between worlds in the Many Worlds interpretation should be made at the level of the mind of an individual observer. I have read that, in this case, each...

Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...

In the section 8-2 dealing with resolving the state vectors, we learn that |\phi \rangle =\sum_i C_i | i \rangle and the dual vector is defined as \langle \chi | =\sum_j D^*_j \langle j |Then, the an inner product is defined as \langle \chi | \phi \rangle =\sum_{ij} D^*_j C_i \langle j | i...

Hi, I have attached the question to this post. I understand on the process on getting to the answer in that you use $$\arrowvert 2, 2\rangle=\arrowvert 1,1\rangle \otimes \arrowvert 1,1\rangle$$ and apply the isospin-lowering operator to obtain $$\arrowvert 2,1 \rangle$$. Then I understand you...

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...

For two different coherent states \langle \alpha|\beta \rangle=e^{-\frac{|\alpha|^2+|\beta|^2}{2}}e^{\alpha^* \beta} In wikipedia is stated https://en.wikipedia.org/wiki/Coherent_state"Thus, if the oscillator is in the quantum state | α ⟩ {\displaystyle |\alpha \rangle } |\alpha \rangle it is...

Hi, so I'm having trouble with a homework problem where it asks me to find the number of states with an energy less than some given E. From this, I was able to work out the energy E to be $$ E = \frac{\hbar^2}{2m} \frac{\pi^2}{a^2} \left( n_x^2 + n_y^2 + n_z^2 \right) $$ and...

Hey, y'all. I know the oxidation state of a carbon in an ethene is -2 while carbon in Acetylene is -1. As well I know acetylene has more disspating elcetrons due to pai bonds. So how come charges between the acetylene carbon are more negative than in ethene while the carbones oxidations states...

Hi everyone, I was attempting the following past paper question below: I have found a value for the coefficient c and I think I have calculated the inner product of <x|x>. I've attached my workings below. But I'm not sure what to do next to answer the last part of the question which asks...

I'm given the following density of states $$ \Omega(E) = \delta(E) + N\delta(E-\Delta) + \theta(E-\Delta)\left(\frac{1}{\Delta}\right)\left(\frac{E}{N\Delta}\right)^N $$ where $ \Delta $ is a positive constant. From here I have to "calculate the canonical partition function as a function of $$...