Questions tagged [quantum-states]
A quantum state is a mathematical entity (abstract geometrical or specific algebraic function) that provides a probability distribution for the outcomes of each possible measurement on a system.
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Quantum measuring simulation
Hi I want to understand a concept that I been thinking about. I'm trying to simulate the energy measurement of a system (a many body quantum system to be precise), and I'm trying to simulate a quantum ...
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What is the difference between "cluster states" and "graph states"?
I wonder about the difference between the cluster state and the graph state.
I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice
The concept of ...
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Is there a physical interpretation of the connection between the scattering matrix and bound states?
The square integrability condition of a scattering wavefunction can be written for imaginary wavenumber $k = -\mathrm{i}\kappa$ as
$$\int_0^\infty \mathrm{d}r\left|(-1)^l \mathrm{e}^{-\kappa r} - S_l(-...
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Fock Space and Coherent state
Can a coherent photon state also belong to the Fock space? If yes, under what conditions? For example I read that
$$\exp\bigg\{-\frac{1}{2}\sum_i|\alpha_i|^2\bigg\}\exp\bigg\{-\sum_i\alpha_ia_i^{\...
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How are we able to use quantum field theory to study systems?
I've been trying to understand the concept of locality in QFT, and I was reading this paper by Edward Witten, where he explains (on pg 13) that the state space cannot be factored into a tensor product ...
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How many states are possible for two (indistinguishable) electrons with $n=2$ in an atom if we forget Pauli’s exclusion principle?
I have been told I can use $^8C_2 = 28$ to obtain the answer to this question, but I am doubtful of this result since I obtain $21$ by simply writing out the possible states as ($ml_{1}$, $ms_{1}$, $...
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Measure probability of collapse instead of collapse itself
I was researching quantum mechanics recently. A particle can be in two states at the same time, with a probability of "collapsing" to one or the other. The example I learned was an electron'...
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Why is the state of a quantum system called "Density $\textbf{Operator}$"?
In quantum mechanics, a $d$-dimensional pure state is represented by a vector belonging to a $d$-dimensional Hilbert space $\mathcal{H}^d$. A mixed state is represented by a density matrix $\rho \in \...
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Clarification regarding the terminology of Microstates
I would like to understand how microstates are defined or used in physics. Are microstates suppose to only mean eigenvalues of a given observable (or a generator of symmetry)? The reason for my ...
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Are the 'wrong' states eigenstates of perturbed Hamiltonian?
Townsend quantum mechanics
In our earlier derivation we assumed that each unperturbed eigenstate $\left|\varphi_{n}^{(0)}\right\rangle$ turns smoothly into the exact eigenstate $\left|\psi_{n}\right\...
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Position and Momentum operators in Heisenberg and Schrödinger picture
The position operator $\hat{x}$ has eigenstates
$$\hat{x}|x\rangle=x|x
\rangle.$$
Usually in the Schrödinger picture the operators are time independent and the states carry the time dependence. ...
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If 2 electrons are entangled $[a] [b]$. if we throw a photon at $-[a]$ will it come out of $[b]-$? [closed]
i was confused as to what will happen when two electrons which are entangled and then if one is exposed to light. will the absorption and emission theory still work and if so how will it work in this ...
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Clarification on the Premises of the Einstein-Podolsky-Rosen Argument
In their famous EPR paper, Einstein, Podolsky and Rosen argue that quantum mechanics does not provide a complete description of physical reality. To do this, they make two key assumptions:
in a ...
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$n$-number of creation operators on the ground state [closed]
I simply want to prove the following:
for the given state, $|n\rangle = \frac{1}{\sqrt{n!}}(a^\dagger)^n|0\rangle$, show that this satisfies $\hat{N}|n\rangle = n|n\rangle$ given $\hat{N} = \hat{a}^\...
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Pauli exclusion principle in case of electron-positron anhillation?
Pauli exclusion principle says that no two particles can occupy a single Quantum state and that prevents electron from falling into the nucleus.
But then, what about electron-positron annihilation, ...
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On the language use of quantum mechanics: "state $\rho$" or "density matrix $\rho$ of the mixed state"?
For pure states one usually uses the bra-ket Notation and then uses language e.g. "the state $|\psi>$..."
Is it also common to say similarly for mixed states, which are usually written as ...
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Why aren't states with 3 basis vectors considered entanglements in two qubit system?
I am going to take out normalization factors for simplicity.
$$|00⟩+|11⟩$$
$$|00⟩−|11⟩$$
$$|10⟩+|01⟩$$
$$|10⟩−|01⟩$$
I can see why these states are entangled but I don't see why the following states ...
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Evolution of a quantum system after decoherence
Decoherence leads to an almost diagonalization of the density matrix of a quantum system (in a certain basis) after an uncontrolled interaction with the environment. How does the quantum system evolve ...
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Sum of operators on superposition state
I'm a little confused about how a sum of operators acting on a superposition state are worked out.
For instance, the superposition of Fock States (photonic)
$$\vert \psi \rangle = \alpha \vert 0 \...
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Doubt in the wave packet formed by superposing plane polarized wave
For a free particle, the plane wave $f(x,t)=e^{i(kx-\omega(k)t)}$ where $E=\bar{h}\omega$ and $p=\bar{h}k$. It satisfies time dependent Schrodinger equation.
But this wave function is not normalizable....
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Difference in density matrix where prob. 1/2 in both $|0\rangle$ and $|1\rangle$ [duplicate]
In my course, we had an example: give the density matrix of a system arising from a proces that generates a [0> with probability 1/2 and a [1> with prob. 1/2. The answer is
$1/2[0\rangle\langle0]...
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Marginalisation of a joint probability distribution in bra-ket notation
Given a wave function $\Psi(\vec r_1, \vec r_2)$, where $\vec r_1$ and $\vec r_2$ are the positions of particle 1 and 2, respectively, the probability of finding particle 1 at position $\vec r$ (...
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States $-|0\rangle$ and $i|0\rangle$ in Bloch Sphere?
I am new on quantum computing and starting reading a book about it. Going through it, the Bloch sphere was described for two states.
My question about is: where are the states $-|0\rangle$ and $i|0\...
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Projection postulate and the state of a system
Quantum Mechanics, McIntyre states the projection postulate as:
After a measurement of $A$ that yields the result $a_n$, the quantum system is in a new state that is the normalized projection of the ...
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What does "coherent evolution" of an $N$-body quantum system mean?
In classical physics we know of coherence of waves and in quantum physics we identify coherent states.
While those are clearly defined concepts/terms, in literature we regularly encouter also that a $...
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Measurement on mixed states
I have a conflict between my lecture notes on quantum mechanics, where it is stated that the probability of measuring an eigenvalue $a_i$ on a mixed state with desnsity matrix $\rho$ is
$$
\...
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For a generic two-state quantum system, are there interpretations for the observables corresponding to all Hermitian operators?
The simplest non-trivial system is a two-level system. Classically, it is a system which can be in one state labelled $H$ or another state labelled $T$. There is no necessary reference to any ...
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How can a basis change make a state suddenly separable?
I am working through my quantum optics textbook by Grynberg, Aspect and Fabre, and this concept has tripped me up a little.
(13) is an inseparable state, whereas (15) IS separable - but they are the ...
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What is a quasibound state and how is it different from a bound state?
What is a quasibound state and how is it different from a bound state?
I have read this term in nuclear physics in the context of compound nucleus formation. A compound nucleus $C$ is formed by the ...
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Creation and annihilation operator in Fock space
In Fock space, the action of annihilation operator $a_i$ on state $N$-particle state $|n_1, n_2, n_3...n_p\rangle$ is directly defined as
$$a_i |n_1, n_2 ..n_i..\rangle = \sqrt{n_i}|n_1, n_2 ...n_i-1.....
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Continuum States in QM
In the Hilbert space of QM, in the finite dimensional case, for a complete orthonormal set of basis vectors, one writes the generic state vector as: $\psi=\sum_j(\phi_j,\psi)\phi_j$. When the complete ...
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Why do we need to normalise states in quantum field theory?
In QM its obvious that we need to normalise quantum states since their inner product squared represents a probability. This normalization leads to physical states in QM being represented by 'rays' of ...
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How to simply explain 'quantum state' to a beginner?
While explaining 'quantum state' to a beginner, is it scientifically accurate to say that "just like '$v$' represents velocity and '$p$' represents the momentum of an object, $|ψ\rangle$ ...
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Bloch sphere representation - rewriting a state
If a quantum state can be represented as
$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$
Then
Because of $|\alpha|^2+|\beta|^2=1$, we may rewrite Equation (1.1) as $$|\psi\rangle=e^{i\gamma}\left(\...
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State Vector vs wave function [closed]
In Dirac's state vector notation, the position representation is given by :
$$ |\psi\rangle = \int d^3r\;\psi(\mathbf{r})|\mathbf{r}\rangle$$
My questions:
Is the State Vector Different from the wave ...
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Reconstructing state from density matrix (and implications for Grover search)
If I am given a density matrix $\rho$ that I know corresponds to a pure state (i.e., $\rho = |\psi\rangle\langle\psi|$ for some $|\psi\rangle$), then is it possible for me to infer the state $|\psi\...
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What do the off-diagonal elements of Hamiltonian matrix physically represent?
A briefly question: what's the "physical meaning" of the off-diagonal elements of Hamiltonian matrix? Such as an Hamiltonian Matraix looks like:
$$\hat H = \begin{pmatrix} E_{11} & E_{12}...
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What is the dimension of two quantum systems with bases $\{a_1,a_2\}$ and $\{b_1,b_2,b_3\}$, combined? [closed]
Quantum system A has a basis $\{a_1, a_2\}$. System B has a basis $\{b_1, b_2, b_3\}$. A and B evolve according to their own Hamiltonian and do not interact at all. If I consider A and B as one large ...
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LOCC distinguishability of a mixture of Bell states
Consider the Bell states
\begin{align}
|\psi^0\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle),& \quad
|\psi^1\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle), \\
|\phi^0\rangle = \frac{...
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Indistinguishability and different pure state decompositions of mixed states in non-simplex convex set of states in Quantum Statistics
In statistical physics (mechanics), the transition from Maxwell-Boltzmann statistics to Bose-Einstein and Fermi-Dirac statistics was motivated by classically inexplicable phenomena such as Bose-...
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What is $\langle 0|p\rangle$?
$\hat{p}$ is the generator of the translation group, so $$|r\rangle=e^{-ir\hat{p}/\hbar}|0\rangle\to\langle p|r\rangle=e^{-irp/\hbar}\langle p|0\rangle.$$ Assuming normalized position states
\begin{...
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What exactly is a Fock state?
I am a bit confused by the way a Fock state is defined and hope to find some clarification.
The Fock space is defined as the direct sum of all $n$-particle Hilbertspaces $H_i$
$$F = H_0 \oplus H_1 \...
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Unitary transformation in rotating frame for two-level atom
Considering an atom with two states: $|g\rangle$ and $|e\rangle$, its Hamiltonian, when illuminating with some drive frequency $\omega_d$, which couples two states (according to wiki):
$$H/\hbar=\...
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Eigenstates of $|x(t)\rangle$
In the Heisenberg picture, operators depend on time. Let $\hat{x}$ be the position operator and
$$\hat{x}(t) = e^{iHt/\hbar}\hat{x}e^{-itH/\hbar},$$
then $|x,t\rangle$ denotes the eigenstate of $\hat{...
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What does the integration of Hamiltonian and the division of a quantum state vector?
In quantum mechanics, specifically schodinger equation, we have $i\frac{d|\psi(t)\rangle}{dt}=H|\psi(t)\rangle$ with $\hbar=1$. If $H$ is time independent, we can solve this equation by first divide $|...
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Intuition behind why density operator contains complete information about the system?
I have read this and I want to know why is that the case, and why not simply write two (or more) particles with their 'pure' states, because the latter is much more straightforward?
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For free fields, is there a one-to-one correspondence between probability distribution of classical field configurations, and states?
If I'm given the field operator of free fields (for example $\phi(x)$) as a function of space time, and a state (for example $\langle 0 | $, I can calculate the expectation value for every point in ...
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What is/are the canonical notation(s) for multi-particle states? What are they mathematically?
I'm trying to refresh things I learned ages ago, and I believe I either never learned the proper mathematical background for multi-particle states or I forgot the details. I intuitively write things ...
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What are dimensions/states in a quantum system?
Since I am just starting out in quantum physics, posing meaningful questions is still hard for me, so please keep that in mind.
First of all, are the dimensions in a quantum system the same as states?
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Negative power in bra-ket notation
While reading for example Nuclear Collective Motion by Rowe, or other materials, I've encountered the notation,
$$\langle m (i)^{-1} | V | n (j)^{-1} \rangle ,$$
where $m, n, i, j$ are particle and ...
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