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The problem is from the book "The Principles of Thermodynamics" by ND Hari dass.
It looks trivial problem, but I am not able to form logical arguements for going into next step.
For example, It seems like first gas has equation of state ##PV =nRT## and second has ## \left( P_2 +\frac{a}{V_2^2}...
Usually states and observables are treated as fundamentally different entities in quantum theory. But are they really different? A state can always be represented by a density "matrix", which is really a hermitian (or self-adjoint) operator. Since observables are also hermitian (or self-adjoint)...
I would like to model squeezed light and its evolution (such as when passing through lenses after being generated) using optics software such as OptiFDTD or ZEMAX. However, I don’t see any way to make such states…my plan was to simulate an Optical Parametric Amplifier to generate these states...
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...
The problem of bound states of an electron trapped in a dipole field is being studied by Alhaidari and company. (See, for example, https://arxiv.org/ftp/arxiv/papers/0707/0707.3510.pdf). It is not clear to me why the point dipole approximation is used everywhere in such calculations. Can't an...
So basically this is how I solved this problem:
1. ##f(x)=\log _{2} x^2 - 1##
2. ##0=\log _{2} x^2 -1 ##
3. ##1= 2\times \log _{2} x##
4. ##\frac{1}{2}= \log _{2} x##
5. ##2^{\frac{1}{2}}=x=\sqrt{2}##
So I wrote coordinates to be (##\sqrt{2}##, 0)
But apparently, that is not the only solution...
I am studying a 2D material using tight binding. I calculated density of states using this method. Can I also calculate partial density of states using tight binding?
I have done part A so far below, but I'm a bit behind on my reading, so I don't quite understand the action of the controlled-NOT gate on a single qubit.
What I have so written so far for part B is:
Let ##\mathcal{H}=(\mathbb{C}^2)^{\otimes 3}##. Let ##|\psi _{q_i}\rangle_k## , ##(i\in\left...
I've already calculated the total spin of the system in the addition basis:
##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...
Hello everyone!
I'm trying to replicate phonon density of states (PHDOS) diagrams for some solids using Quantum Espresso. The usual way I do it is the following one:
scf calculation at minima (pw.x)
Calculation of dynamical matrix in reciprocal space with nq=1 or 2 (ph.x)
Calculation of...
$$n = \sqrt{n_x^2 + n_y^2 +n_z^2}$$
$$E = \frac{n^2 \pi^2 \hbar^2}{2mL^2}$$
$$n = \sqrt{ \frac{2mL^2E}{\pi^2 \hbar^2} }$$
This is all given by the textbook.
It's even as friendly as to say
$$\text{differential number of states in dE} = \frac{1}{8}4 \pi n^2 dn$$
$$D(E) = \frac{...
I'm reading "Statistical Mechanics: A Set of Lectures" by Feynman.
On page 1 it says that, for a system in thermal equilibrium, the probabilities of being in two states of the same energy are equal. I'm wondering if this is an empirical observation or if it can be derived from QM?
I am trying to find the expected value of the variance of energy in coherent states. But since the lowering and raising operators are non-hermitian and non-commutative, I am not sure if I am doing it right. I'm pretty sure my <H>2 calculation is right, but I'm not sure about <H2> calculation...
By considering the power series for ##e^x##, I assert that ##N=e^{-\lambda^2/2}## and that ##a\Psi_\lambda = \lambda \Psi_\lambda##. Because the Hamiltonian may be written ##\hbar \omega(a^\dagger a + 1/2)##, ##\langle E \rangle = \hbar \omega(\langle a \Psi_\lambda, a \Psi_\lambda \rangle +...
Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways:
$$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$
and
$$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$
where it must be understood that this expression is...
Let's say atom has two energy levels, ##E_1## and ##E_2##. If atom is in the first state ##|E_1\rangle##, then it's able to absorb a photon with energy ##E_2-E_1##, while transitioning to the second state ##|E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding...
A photon in QFT is defined in the same way as all particles. That is they denote a set of quantum states that transform in the simplest possible way under Poincaré transformations. Properly this is known as an irreducible representation (irrep) of the Poincaré group. You can classify these...
For a state to be stationary it must be time independent.
Naively, I tried to find the values of c where I don't have any time dependency.
##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...
What I have done is the following:
\begin{equation}
\braket{\eta_k | \eta_k}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\bra{0}(A^{\dagger})^nA^n\ket{0}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\int...
It is "easy" to produce experimental setups that could and should for all practical purposes be described as having a constant background magnetic field everywhere, especially in the "asymptotic region" where the detectors are located.
You can do this both in vacuum, and inside a solid sample...
If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be...
This thread is meant to discuss a topic that arose in https://www.physicsforums.com/threads/is-there-a-theoretical-size-limit-of-a-planet.1045983/ in a more precisely specified, idealized way.
Further details:
1) Standard model + GR assumed, no other theories intended for this...
Hello! If we have a 2 level system (I will call the states g and e for ground and excited), and a laser field (which can have any detuning relative to the spacing between g and e), it can be shown that that the total number of particles is conserved under the laser-atom interaction hamiltonian...
Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...
Quantum states are most often described by the wavefunction ,##\Psi##. Variable ,##\Psi(x_1x_2\dots x_n) \Psi^*(x_1x_2\dots x_n)## defines probability density function of the system.
Quantum states can also be described by the density matrices (operators). For a pure state, density matrix is...
I just happened to hear this one night last week. It is a history of the US from the perspective of two historians from the early 20th century.
https://librivox.org/history-of-the-united-states-vol-i-by-charles-and-mary-beard/
https://librivox.org/group/495
I was listening to this around the...
There is a passage in this book where I don't follow the logic;
In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman
\mathcal{A} represents the apparatus that is performing the measurement
the apparatus can be oriented (in principle) in...
I'm reading about Bloch states, these the are states of electrons in a periodic potential. What i know is that the electron in a Bloch state is shared between many ions and it is a stationary state.
However, for a 1-dimensional model I've read that at the edge of the first Brillouin zone, when...
hi guys
my nuclear physics professor gave us a hand written notes about a the isospin multiplets of elements, the notes provides a brief not clear introduction to the topic with some formulas for calculations, as following
$$
E_{xe} = \Delta\;E_{B}+\Delta\;E_{c}
$$
$$
\Delta\;E_{B}=...
It is commonly said that the phase of coherent states can't be measured, just the relative phase between two coherent states.
A qubit example: define the states
$$|\phi\rangle=[|0\rangle+\exp (\mathrm{i} \phi)|1\rangle] / \sqrt{2}$$
and the measurement operators...
Summary: Determine the absorbing states & communication classes of the given matrix.
Hello everyone,
If we have a state space of S = {1,2,3,4} and the following matrix:
\begin{bmatrix}
0 & 1 & 0 & 0\\
0 & 0 & 1/3 & 2/3\\
1 & 0 & 0 & 0\\
0 & 1/2 & 1/2 & 0\\
\end{bmatrix}
Now, given the...
If I have two identical particles of ##1/2## spin, for Pauli's exclusion principle all physical states must be antysimmetrical under the exchange of the two particles, so ##\hat{\Pi}|\alpha\rangle=-|\alpha\rangle##. Now, let's say for example this state ##\alpha## is an Hamiltonian eigenfunction...
Hello, How come in XPS the binding energy gaps between oxidation states of vanadium oxide are not equally spaced? Is there a reason they are not all equally spaced? V2+ (VO) 513.0 eV V3+ (V2O3) 515.6 eV V4+ (VO2) 516.0 eV V5+ (V2O5) 517.1 eV Many thanks
Summary:: How to calculate qubit states with the Schrodinger eq
I'm writing something about the relation between quantum computers and the Schrodinger equation. One of the requirements is there has to be an experiment. So I thought I could measure some qubits that have results and then do the...
The possible forms of solids can be more than just amorphous solids and crystalline solids. I tried a look at a couple of wikipedia articles and one of them showed descriptions of Plasticity, elastic, and Viscoelasticity, but those are not enough. I can only think to give some real world...
I am a little lost on how to approach this problem.
What I know is the following:
The r vector is in terms of x y and z hat.
I know my two l=0 states can be the 1s and 2s normalized wave function for Hydrogen.
Should I be integrating over dxdydz?
Hello there, I am having trouble understanding what parts b-d of the question are asking. By solving the Schrodinger equation I got the following for the Landau Level energies:
$$E_{n,k} = \hbar \omega_H(n+\frac 12)+\frac {\hbar^2k^2}{2m}\frac{\omega^2}{\omega_H^2}$$
Where ##\omega_H =...
I'm trying to figure out the second order extension of the "trick" used on page 92 (https://www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf) for the calculation of the effective mass matrix ##m^{\star}_{ij} = \hbar^2 (\partial^2 E/ \partial k_i \partial k_j)^{-1}## on page 94. I think for this one...
Hello, I work with a spectrometer that does ionizations through laser 2+1 photons resonant ionization (a high power narrow bandwidth laser is tuned to a precise wavelenght so that it allows reaching an excited energy level of a particular element with the sum of two photons absorbed...
https://en.wikipedia.org/wiki/Observability
I am studying observability and I try to get some intuition on the topic.
Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a...
In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere.
That is, if the general state of the spin system
, (1)
then, according...
I tried to find states in direct method using ##\frac{E}{E_0}=\:nx^2+ny^2+nz^2## and ##100\:<nx^2+ny^2+nz^2\:<\:136##
But it was too long, found it using phi approximation there are around 300 energy states, and Python find around 271 states using direct method but I need manual or recursive...
To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...
If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...
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...
This is a spring problem
From this, it says I need to answer in terms of kinematic friction which to me doesn't make much sense. I also looked at similar questions online to the "in terms of" problems and they don't use all four variables in their derived equation. Do I not need to use all...
Hi I'm new to quantum mechanics, Looking for some help regarding a concept i am struggling to solve. I am curious if I had a cube of particles in a ground state and another cube with the same particle in a higher energy state.
If I placed one upon another, is there anything in quantum mechanics...
In the following pdf I tried to calculate the density of states of free electrons and phonons. First, I found the free electron DOS in 1D, it turns to be proportional to (energy)^(-1/2) and in 2D it is constant. However, I am not sure I found the DOS for phonons in the second part of the...