All Questions
Tagged with quantum-mechanics reference-request
47
questions
9
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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 ...
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Quantum mechanical books for mathematicians
I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential ...
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3
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Books on Perturbation Methods
I am having problems finding descent books on perturbation methods. I am looking for a book which covers; asymptotic expansions, matched Asymptotic expansions, Laplace's Method, Method of steepest ...
- 15k
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0
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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-...
- 4,624
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1
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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 ...
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3
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0
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170
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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 ...
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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 ...
CommunityBot
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3
votes
2
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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 ...
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5
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2
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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:
$$\frac{-\hslash^2}{2m}\psi''(x)-V_0\delta(x)\psi(x)=E\psi(x)$$
...
- 13.8k
0
votes
1
answer
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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 ...
- 6,077
9
votes
1
answer
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Complementary text for mathematical Quantum Mechanics lectures
I'm looking for a text to complement Frederic Schuller's lectures on QM. His approach is very mathematical -- in fact it looks like the first 12 of 21 lectures are just about the mathematical ...
- 4,021
3
votes
2
answers
751
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Expectation value of pure state in quantum mechanics
It's well known that in quantum mechanics, the expectation value of a self-adojint operator $A$ in pure state $|\psi\rangle$ is $\langle\psi |A|\psi\rangle = \operatorname{Tr}(A |\psi \rangle \...
- 4,021
8
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1
answer
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How to find interesting operators for a quantum system?
How can we find "interesting" operators for a quantum mechanical system?
I can think of the following method: Given some system with an associated Hilbert space $V$ and Hamiltonian $H:V\rightarrow V$,...
- 4,021
10
votes
1
answer
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Derivation of Schrödinger's equation
I recall a famous quote of the late physicist Richard Feynman:
Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.
This quote ...
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