Questions tagged [quantum-mechanics]
For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales.
1,732
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Problems in deriving the upper bound of quantum noise induced barren plateau phenomenon
I have got the main ideas of paper Noise-Induced Barren Plateaus in Variational Quantum Algorithms, but the process of proving the theorem 1 in supplementary note 2 has got me really confusing. ...
- 11
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How to Solve the Differential Equation Involving Pauli Matrices and Time-Dependent Terms?
I am trying to solve the following differential equation analytically`:
$$
{\rm i}\,\partial_{t}
\begin{pmatrix}
u^{+}
\\
u^{-}
\end{pmatrix} =
\left[\rule{0pt}{5mm}\,2\alpha
\left(n - vt\right)\sigma^...
- 41
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Stochastic differential equations with only time integrals
I want to reason about the stochastic differential equation
$$ dX_t = A_t X_t dt $$
Where $A_t$ is a matrix valued stochastic process, and hence $X_t$ is a vector valued stochastic process. Are there ...
-1
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Theoretical and mathematical explanation on calculating magnetic moment of materials in quantum mechanics [closed]
Could someone please provide a comprehensive and in detail theoretical explanation of how to calculates the magnetic moment of a material(total magnetic moment and absolute magnetic moment) of a ...
1
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Some details concerning projective representations in Wienberg's book
I have a question from the book "the quantum theory of fields" by S. Weinberg in page 89:
How can we get $[U(\Lambda )U(\bar{\Lambda})U^{-1}(\Lambda \bar{\Lambda})]^2=1$ from the fact that ...
- 763
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56
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Differentiation under integral signs as done in basic quantum mechanics
In various text books, lectures or lecture notes on basic quantum mechanics, I've seen cases differentiating under integral signs and I am wondering why it is allowed in those situations.
The typical ...
- 2,436
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33
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Kraus operators
Suppose we have a POVM given by the family of positive, hermitian operators $\{E_i\}_{i\in I} \in \mathcal{H}$.
From the Neimark dilation theorem we know that the given POVM can be obtained from ...
- 75
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Does the trace of an operator commute with time derivatives of an operator?
I want to find the rate of entropy production in a quantum system using von Neumann entropy $$S = -tr{(\rho \ln{\rho})}$$ by taking it's time derivative. Can I take the derivative inside the trace or ...
1
vote
1
answer
62
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Eigenvalues of superoperators and their Choi matrices
It is well known that $\Phi$ is a completely-positive and trace-preserving (CPTP) map if and only if the corresponding Choi matrix $C_\Phi:=\sum_{i,j} E_{i,j}\otimes \Phi(E_{i,j})$ is positive semi-...
- 393
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2
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Von Neumann entropy vs Shannon entropy
Let us consider a mixture of quantum states
$$
\rho = \sum p_{i}\left\vert \psi_i\right\rangle \left\langle\psi_i\right\vert\quad
\mbox{probability distribution}\,\,\, p_{i}
$$
If the $\psi_{i}$ form ...
- 21
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3
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79
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Completeness meaning (complete basis vs complete metric space)
Today my professor started talking about the formalism of QM.
We talked about the eigenvectors of a Hermitian operator (over Hilbert space) as a "complete set". He also mentioned briefly ...
- 389
-1
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1
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49
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Quantum Computing: Quantum teleportation circuit [closed]
Given the following quantum teleportation circuit. It is required to calculate $\psi_i$ for $i=\{1,...,6\}$.
My answer for
$\psi_3 = [\alpha/2,\beta/2,\beta/2,\alpha/2,\alpha/2,-\beta/2,-\beta/2,\...
- 1
1
vote
1
answer
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Understanding the Relationship Between the Principal Symbol of $-\Delta$ and $\sqrt{-\Delta}$ and Geodesic Flow in Hamiltonian Systems
In the context of Hamiltonian systems in symplectic and Riemannian geometry, consider the following fact: Let $(M,g)$ be a Riemannian manifold and $(M,\omega,H)$ a Hamiltonian system with $$H(q,p)=\...
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Why does it seem like two parameters $k_1$ and $k_2$ are needed to match $e^{-r}$ and $k_2\sin(k_1\,r)$ as well as their derivatives $\frac{d}{d\,r}$?
The Spherical Bessel functions that solve the Spherical Helmholtz equation in the Spherical Coordinate system come in four kinds, the Spherical Bessel Functions of the first kind, the Spherical Bessel ...
- 951
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Quantum Ergodic Theorem: why $\sqrt{-\Delta}$ is used instead of $-\Delta$?
I'm studying the proof of Quantum Ergodic Theorems in the book Partial Differential Equations II: Qualitative Studies of Linear Equations (3rd edition) by Michael E. Taylor. The book includes the ...
- 323