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Results tagged with quantum-mechanics
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user 32389
For questions about mathematical problems arising from quantum mechanics, a branch of physics describing the behaviour of nature at very small scales, at the level of atoms and subatomic particles.
3
votes
Integrals of two Bessel functions of the first kind and a modified bessel function of the se...
The integral should be calculable by the Mellin-transform technique. See the calculation of the similar (but different) integral in http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-7-7-1218 …
- 16.5k
0
votes
Space with 720° / not 2$\pi$ rotational symmetry?
Not only spinors can be used to demonstrate that $360^\circ$ rotation is not an identity transformation. See http://www.maa.org/sites/default/files/pdf/upload_library/22/Hasse/00029890.di991816.99p060 …
- 16.5k
3
votes
Appropriate Recursion relations for Wigner 3j Symbols
Try these references http://scitation.aip.org/content/aip/journal/jmp/16/10/10.1063/1.522426?ver=pdfcov (Exact recursive evaluation of 3j‐ and 6j‐coefficients for quantum‐mechanical coupling of angula …
- 16.5k
3
votes
Quantum Mechanics derivation of Wallis' Formula?
Actually, to prove that $$\lim_{n\to\infty}\frac{n^2}{n+\frac{1}{2}}\left[\frac{\Gamma(n)}{\Gamma(n+\frac{1}{2})}\right]^2=1,$$
there is no need in the Bohr's correspondence principle. Stirling's Seri …
- 16.5k
1
vote
Accepted
Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions
It seems the following two articles http://arxiv.org/abs/1110.2122 (A simple derivation of the Lindblad equation, by Carlos Alexandre Brasil, Felipe Fernandes Fanchini, Reginaldo de Jesus Napolitano) …
- 16.5k
2
votes
Resource for learning quantum mechanics from the viewpoint of representation theory
Basic foundations of quantum mechanics in a representation theoretic language can be found in van den Ban's lectures "Applications of representation theory in classical quantum mechanics" at this page …
7
votes
Applications of Jordan algebras
Jordan algebras were originally introduced by Pascual Jordan in a hope to generalize the orthodox formulation of quantum mechanics, but this program was not successful as far as the generalization of …
- 16.5k
1
vote
Quantum Mechanics and bilinear optimal control theory
In addition to the literature indicated by Carlo Beenakker: in this 2015 review http://arxiv.org/abs/1508.00442 (Training Schrödinger's cat: quantum optimal control, by S.J. Glaser et al.) the authors …
- 16.5k
4
votes
Accepted
Closed form for 3j-symbol ratios
The following recursion relation
$$
C(m_2+1,m_3-1)\begin{pmatrix}l_1 &l_2 &l_3\\m_1&m_2+1&m_3-1\end{pmatrix}+
D(m_2,m_3)\begin{pmatrix}l_1 &l_2 &l_3\\m_1&m_2&m_3\end{pmatrix}+$$ $$
C(m_2,m_3)\begin{p …
- 16.5k
1
vote
Accepted
Reference request: a guide through quantum probability
If you are interested in quantum probability from mathematical perspective, these two books will be helpful:
http://www.springer.com/mathematics/probability/book/978-3-540-60270-5 (Quantum Probabilit …
- 16.5k