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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
6
votes
Quantum Hamiltonian for an Inverse Cube Force Law
In addition to the Carlo Beenakker's answer: the following paper http://arxiv.org/abs/0903.5277 (Self-adjoint extensions and spectral analysis in Calogero problem, by D.M. Gitman, I.V. Tyutin and B.L. …
3
votes
Self-adjoint extensions and delta potentials
Maybe the following references will be helpful:
http://arxiv.org/abs/quant-ph/0103153 (Self-adjoint extensions of operators and the teaching of quantum mechanics, by G. Bonneau, J. Faraut and G. Vale …
2
votes
What are the applications of Grillakis Shatah and Strauss paper?
Maybe the following review article http://www.ams.org/journals/bull/2009-46-01/S0273-0979-08-01228-7/home.html (Why are solitons stable? by Terence Tao) will be helpful.
Some applications of the soli …
2
votes
About an integral equation
As was indicated in the answer at https://math.stackexchange.com/questions/1021510/about-an-integral-equation, you can transform your integral equation into the second order differential equation. Som …
3
votes
Self-adjoint operator
See pp. 231-232 in Birman M.S., Solomyak M.Z. Spectral Theory of Self-Adjoint Operators in Hilbert Space (Reidel, 1987).
1
vote
Schrödinger operators on a sphere
From mathematical side, spectral problem for zonal Schrödinger operators on n-spheres is studied in http://projecteuclid.org/euclid.cmp/1104200938 (Zonal Schrödinger operators on the n-sphere: invers …
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 …
2
votes
$\zeta$-function regularized determinants
Of course that $1+2+3+4+\ldots =-1/12$ is a "correct" result is somewhat mysterious, as the following excerpt from Ramanujan's second letter to Hardy lively demonstrates:
"I was expecting a reply …
0
votes
Reference request for Stieltjes Transform
Maybe the following reference will be useful https://arxiv.org/abs/1105.0060 (Signal Processing in Large Systems: a New Paradigm, by R. Couillet, M. Debbah). See also chapter 3 in the book "Random Mat …
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 …
2
votes
Resource recommendation: Spectral theory and $C^*$ algebras
Maybe the following book will be useful: http://www.springer.com/us/book/9788847028340 (Spectral Theory and Quantum Mechanics, by Valter Moretti).