States Definition and 1000 Threads

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 $$...

I am confused about the relation between the number state ##|n\rangle## with the annhilation and creation operators ##a^\dagger## and ##a## respectively, and the number of atoms in the harmonic oscillator. I'll try to express my current understanding, I thought the number states represent the...

Most undergrad textbook simply say that it is intuitive that boundary conditions should not play a role if the box is very large. Other textbooks suggest that this should be taken for granted since the number of particles at the surface are orders of magnitude smaller that the number of bulk...

Hello! I am reading about excited levels in nuclei (I am mainly following Wong's nuclear physics book) and I am a bit confused about the nature of the excited states. In the one particle picture (mainly shell model) the excitation appears as static i.e. one nucleon moves from a certain orbital...

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...

i am reading this paper . in the definition 19 we have |z><z| = :exp(a-z)^\dagger (a-z): in the extansion the first term is the identity son it is not hart to find an eigenvector for the value 1. it is ok if the vector is annihilated by a. if is the case for the coherent grouns state. how to...

the answer is NE^0.5 but my answer is E^0.5N the # of state is Ω=( one particle phase-space volume)^N one particle phase-space volume=integration of dq*integration of dp from space part dq I get V and dp is converted into Energy E variable via E=p^2/2m

Hello! How are the parity and spin of excited states of nuclei measured experimentally. I imagine that the energy can be easily measured by exciting the nucleus (by colliding it with a nucleon or electron for example) and then measuring the emitted photons. But how can one infer the spin and...

Hello, I would like to understand as well as possible what (quantum) coherent states are. Can anyone advise on what books (or other materials) I should read? Please assume I have an introductory level in Quantum Physics (where by "introductory" I mean the material introduced in books like, for...

Resources I have looked at distinguish between the three basic states of matter in terms of how closely particles are held together; i.e. in solids they are bound most closely, in liquids less so and in gases they're much freer. Would it not be more correct to refer to how closely atoms or...

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...

$$<p_1 p_2|p_A p_B> = \sqrt{2E_1 2E_2 2E_A 2E_B}<0|a_1 a_2 a_{A}^{\dagger} a_{B}^{\dagger} |0>$$ $$=2E_A2E_B(2\pi)^6(\delta^{(3)}(p_A-p_1)\delta{(3)}(p_B-p_2) + \delta^{(3)}(p_A-p_2)\delta^{(3)}(p_B-p_1))$$ The identity above seemed easy, until I tried to prove it. I figured I could work this...

https://www.wired.com/story/a-bizarre-form-of-water-may-exist-all-over-the-universe/ Black iceI knew the Black Ice Theories since around 1990 https://www.nature.com/articles/s41586-019-1114-6 -- Demontis, P., LeSar, R. & Klein, M. L. New high-pressure phases of ice. Phys. Rev. Lett. 60...

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...

I can solve the two particle system easily enough: Using ##j_1 = 1## and ##j_2 = 1##, the possible total angular momentum values are ##j = 2, 1, 0##. With ## m = -j , -j+1, ..., j ##, ##j = 2: m = 2, 1, 0, -1, -2 ## (5 states) ##j = 1: m = 1, 0, -1## (3 states) ## j = 0: m = 0 ## (1 state) I...

In principle, unbound states exist when ##E \gt V## at infinity. Are these unbound states just for calculation, or can we physical realize unbound states? After all, an unbound state means its possibility at infinity is not zero, and it seems impossible to realize such a state.

Reduced graph states are characterized as follows from page 46 of this paper: Proposition: Let ##A \subseteq V## be a subset of vertices for a graph ##G = (V,E)## and ##B = V\setminus A## the corresponding complement in ##V##. The reduced state ##\rho_{G}^{A}:= tr_{B}(|G\rangle\langle G|)## is...

The dubious assumption I am making is that the integral over the density of states is proportional to the volume in k space. Since $$\epsilon=\frac{(\hbar)^2k^2}{2m}$$ for part a, and $$\epsilon=(\hbar)\omega k$$ for part b, and $$V\propto k^d$$ for d dimensions in k space. So, $$\int...

In most standard exposition of (the mean-field theory of) charge density wave (CDW), phase and amplitude fluctuations are introduced as the collective excitations. Kohn anomaly in the acoustic phonon dispersion is also mentioned as temperature goes from the above till the CDW transition...

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How did you find PF?: internet question about electron triplet states I'm a retired accelerator physicist entertaining myself by trying to understand physics questions like entanglement better. I calculate the expectation value of the product of two electron spins in the singlet state with...

I just want to clear some confusion I am having with the Fermi-Dirac distribution & density of states (DOS) of a semiconductor, which are given by Say we have a piece of Silicon in equilibrium and its Fermi level lies 0.25 eV below the conduction band edge, i.e. Ec - EF = 0.25 eV. Let us say...

And when we act on such a direct product with the sigma (Pauli) matrices, and sigma+ and sigma-, we act on the individually, is that right? Thank you! PS. this is NOT homework help, term hasnt even started and this is a past question sheet. Also, I have answers, but they are brief and...

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...

I know that we use quantum mechanic and wave function to calculate probability of finding electrons but is there anything valid about bohr model that we still use it?

Because massive gauge bosons have a finite half life, are they excluded from the (infinitely, asymptotically remote?) in and out states of QFT? Or, to put it another way, are they restricted to the internal legs of Feynman diagrams, i.e. to being virtual only? We can see W and Z tracks in...

suppose we are working on a step potential problem, and two transmitted wave functions,corresponding to one particle, are obtained. Let's name them ##|1>## and ##|2>##. How can we interpret physically the case where ##<1|2>##=##-<2|1>##? or in position...

Summary: specific modulation of lasers will cause ionisation, how is this being used in plasma physics? Just a simple question

Hello. I have a question. In the book I am reading, They derive the Ubs operator applied on a photon state with the beam splitter at a ratio of 50/50. A beam splitter that is used in the Mach-Zehnder interferometer. I'm having a hard time deciphering whether the formula for beam splitter...

Weinberg writes in his book on QFT Vol1 that bound states in QED are problematic because perturbation theory breaks down. consider the case of hydrogen atom, electron+proton. Weinberg explains this case and I copy from the book: https://www.physicsforums.com/attachments/247655 what is time...

Since my major is not physics. My QM knowledge is not pretty good (Mostly self study). I am sorry if this question was asked multiple times in the forum. I've learned that wavefunction can be written as a linear combination of eigenfunctions due to completeness property. If an electron is...

I was looking for a derivation for the density of states and I came across this page: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm I followed the derivation and came up with: g(E) = (1/L3)dN/dE = (1/L3)L3/∏2*k2 * dk/dE =K2/∏2 * dk/dE =K2/∏2 * g(E) =...

I have a question on tensor-product states that I'd like to ask, thanks in advance! 1. The basis vector of a two-particle state can be written as ##|\mu_i \rangle |\nu_j \rangle## for orthonormal vectors ##|\mu_i \rangle, |\nu_j \rangle## spanning their single-particle Hilbert spaces. The inner...

Is it possible to solve the problem of which quantum mechanical interpretation is true, by sending the brain super imposed quantum mechanical signals. The individuals, perception of the signals, could identify which interpretation is correct. Could, an experiment of some sort be formulated with...

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...

The multiplicity of states for a particle in a box is proportional to the product of the volume of the box and the surface area of momentum space. $$ \Omega = V_{volume}V_{momentum}$$ The surface area in momentum space is given by the equation: $$p^{2}_{x}+ {p}^{2}_{y}+{p}^{2}_{z} =...

Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...

Using the fact that Pa ∝ |α|^2 and Pb ∝ |β|^2, we get: Pa = k|α|^2 and Pb = k|β|^2 Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get: Pa = |α|^2/(|α|^2 + |β|^2) and Pb = |β|^2/(|α|^2 + |β|^2)...

Well, I have no clues for this problem. Since I can get nothing from the definition of ##\rho##, I tried from the right part. Also, I know that ##\left ( \vec r \cdot \vec \sigma \right ) ^2={r_1}^2 {\sigma _1}^2+{r_2}^2 {\sigma _2}^2+{r_3}^2 {\sigma _3}^2##. Plus, ##\rho## is positive; then...

Considering a mixture ##\sum p_i|\Psi_i\rangle\langle\Psi_i|## This does not describe an ensemble of quantum systems since the particle number is defined by ##\Psi_i##. The question is in the continuous wave-mechanical formalism where I don't understand what object the density matrix is : I...

Coherent states are eigen state of lowering operator ##a## |\alpha\rangle=e ^{-\frac{|\alpha|^2}{2}}\sum^{\infty}_{n=0}\frac{\alpha^n}{\sqrt{n!}}|n \rangle , where ##\{|n \rangle\}## are eigenstates of energy operator. What is the case of state ##|0 \rangle##? a|0 \rangle=0|0 \rangle=0. So...

I hope my articulation makes sense. Can I prepare a particle so that it has >1 states in superposition and resolve them at different times? I will make up states to try and illustrate my question better. Prepare a particle so that spin up and spin down are in a state of superposition. Also...

Hello, I've recently been admitted to the MSc QFFF program at Imperial College London for the 2019-2020 year and am seeking advice regarding possible career paths/was wondering if anyone is in a similar situation. My end goal is to do a PhD in the United States since (for non-academic reasons)...

Could it be possible that using a mixed stated ##\rho=\sum_{i=1}^4|\langle e_i|\Psi\rangle|^2|e_i\rangle\langle e_i|## Where ##\Psi## is the singlet state and the ##e_i## form an orthonormal basis (like an intermediary state),That one could violate Tsirelson's bound if the parameters describing...

We can consider the ammonia molecule ##NH_{3}## a two level quantum system, because the ##N## atom can be either above or below the plane formed by the three ##H## atoms. We call these states ##|+ \rangle## and ##|- \rangle##, respectively. The hamiltonian in the basis ##(|+ \rangle, |-...

Number of states in that volume of k-space, ##n(k)dk## is: $$n(k)dk = (\frac{L^3}{4 \pi^3}) \cdot 4 \pi k^2 dk = \frac{L^3}{\pi^2}dk$$. Then the notes state that by defintion, ##n(k)dk = n(E)dE##, and hence $$n(E)d(E) = \frac{L^3}{\pi^2}dk$$. I don't quite see why this is true - isn't it the...

I'm working on some stuff for particle physics and I had a few questions I wanted to ask . Heres the outline of the problem : Establish which initial states of the ppbar system amongst 1^S_0, 3^S_1, 1^P_1, 3^P_0, 3^P_1, 3^P_2, 1^D_2, 3^D_1, 3^D_2, 3^D_3 the reaction ppbar->npi^0 can...

Hello! Given an excited state of a nucleon, such as the ##\Delta## baryon (and here I mean all its 4 version ##\Delta^{++}##, ##\Delta^{+}##, ##\Delta^{0}##, ##\Delta^{-}##), the decay channel is (in this case) to a pion and a nucleon. I was wondering, is the decay probability the same for all 4...

Homework Statement A bacteria that normally divides every 20 minutes express gene X. The production rate of protein X is 5nM/min. The protein is stable and does not degrade. What is the concentration of X in the steady state?The same bacteria enter into a stress state at t=0 for 3 hours...