Questions tagged [quantum-mechanics]
For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales.
1,729
questions
1
vote
0
answers
31
views
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
2
votes
0
answers
36
views
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
42
views
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
1
vote
2
answers
70
views
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
0
votes
3
answers
74
views
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
votes
1
answer
48
views
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
48
views
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)=\...
- 323
2
votes
0
answers
83
views
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 ...
- 911
1
vote
0
answers
58
views
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
0
votes
0
answers
121
views
Apparent or real contradiction is in Eberlein's paper?
The questions I pose here concerns the paper "The Spin Model of Euclidean 3-Space" by W. F. Eberlein (The American Mathematical Monthly, Vol. 69, No. 7 (Aug. - Sep., 1962), pp. 587-598) (...
- 2,065
1
vote
0
answers
55
views
Are there any useful convexity properties of quantum dynamical semigroups?
I'm am wondering if there are any useful properties of quantum dynamical semigroups I can exploit for convex/concave optimization with respect to the semigroup parameter. A proper definition of a ...
- 85
0
votes
0
answers
20
views
Restrictions on a set to be the spectrum of a 1D (discrete) Schrödinger operator.
What restrictions are there on a compact set $E\subset\mathbb{R}$ for $E$ to be the spectrum of a bounded (discrete) Schrödinger operator on $l^2(\mathbb{Z})$? Is there a known necessary and ...
- 1,035
2
votes
1
answer
57
views
A question on geometric quantization
Assume $(M,\omega)$ is a symplectic manifold. Consider $H$ to be the space of complex wavefunctions on $M$, $\{ \psi: M\to \mathbb{C}\}$ with scalar product given by $\langle \psi |\phi \rangle =\int_{...
- 759
1
vote
0
answers
119
views
Are quasi-sets (and therefore Schrödinger logic(s)) studied by mathematicians or are they purely in the domain of philosophers?
Context:
I'm a fan of different kinds of logic. I'm conflicted about whether different logics actually exist beyond, say, a philosophical oddity.
The Question:
Are quasi-sets (and therefore ...
- 45.7k
0
votes
0
answers
26
views
Spectral analysis for harmonic oscillator operator?
Let $L=-\frac{d^2}{dx^2}+x^2, x\in\mathbb R$, the one-dimensional harmonic oscillator; this is an unbounded self-adjoint operator acting in $L^2(\mathbb R)$.
I am looking for a reference that deals ...
- 1,691