All Questions
Tagged with quantum-mechanics reference-request
47
questions
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Quantum Mechanical PDE Question
I'm studying quantum mechanics and I'm considering the usual time-independent Schrödinger equation
\begin{equation*}
-\left(\frac{\hbar^{2}}{2m}\right)\left(\nabla'\right)^{2}u_{E}(\mathbf{x}') + V(\...
- 11
3
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2
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General definition of POVM
Wikipedia gives the following definition of positive operator-valued measure (POVM):
A POVM on a measurable space $(X,M)$ is a function $F$ defined on $M$ whose values are bounded non-negative self-...
- 759
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Mathematical Foundations of Quantum Mechanics
As the title says, I am interested in a textbook/reference that deals exclusively with the mathematical foundations of quantum mechanics, without (or, with minimal) physics involved.
As an example on ...
- 103
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Understanding the free will theorem
I am trying to understand the mathematical content of the free will theorem. See this link or just the wikipedia pages and the references therein.
I think the main point of the theorem is the ...
- 2,719
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Are there any theorems that can only be explained by analogies requiring knowledge of quantum mechanics?
The theorems I’ve seen in analysis can be explained by analogies that invoke the macroscopic visible world, areas, volumes, life sized physical things in sets. Are there any theorems in math that if ...
user739402
3
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2
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350
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Extension of Choi-Jamiolkowski isomorphism to not completely positive maps
In quantum physics, the concept of Channel-State duality is of prime importance in understanding the final state of the system after passing through a channel or performing quantum operations. The ...
- 587
5
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2
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1k
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Schrödinger equation involving the Dirac-Delta
I am taking a course on quantum mechanics and I try to understand the time-independent Schrödinger-equation with the Delta-potential:
$$\frac{-\hslash^2}{2m}\psi''(x)-V_0\delta(x)\psi(x)=E\psi(x)$$
...
- 2,437
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3
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Mathematically rigorous Quantum Mechanics
I am a student of mathematics attending a course in Quantum Mechanics. This course is held by a physicist, and it is really confusing for me to follow his reasonments. With this, I do not mean to be ...
- 2,532
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Reference request for operator theory in Quantum mechanics
I am studying Shankar's Principles of Quantum Mechanics. In the first chapter where the author introduces the necessary mathematics tool for QM, the concept of derivatives of operators with respect to ...
- 999
5
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3
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190
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Reference request: representation focused view of quantum mechanics
I'm interested in learning a bit more about quantum mechanics from a more Lie algebra/representation theoretic perspective, hopefully including but not going past quantum field theory.
I was ...
- 1,903
3
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1
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Reference request for quantum Teichmuller space
I would like to ask for some detailed reference for quantum Teichmuller theory, better in a mathematical taste. I read a little bit on Kashaev's or Chekhov and Fock's, but find that I need to fill ...
- 749
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Computing Complex Ito calculus for stochastic process
Let $X_t$ be a stochastic process in $\mathbb{C}^n$ such that
$$ dX_t = a(X_t,t)dt + b(X_t,t)dW_t.$$
And let $f:\mathbb{C}^n \to \mathbb{C}$.
Then how to compute $df(X_t)$ in complex?
If $f$ is a ...
- 1,964
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1
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594
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What h.c. stands for?
I came across the following equation
$$ A = UAV + h.c. $$
For example, please see Eqn (2) in here.
But I have no idea what h.c. stands for... It seems that it comes from some physics.
Any comments ...
- 1,964
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Hilbert space theory and their applications
What are the best books that discuss the theory of Hilbert spaces and their applications to quantum mechanics for the beginners
- 2,498
6
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673
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Quantum Chemistry book recommendation. [closed]
I am trying to learn quantum chemistry. I have an extensive background in math and physics, so I'm looking for a book that makes full use of whatever physics and mathematics is relevant to this ...
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