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Results tagged with fa.functional-analysis
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user 20729
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
15
votes
2
answers
1k
views
Is zero a hydrogen eigenvalue?
This question has been bugging me for some time.
Take the hamiltonian for the hydrogen atom: $$\hat{H}=-\frac{1}{2}\nabla^2-\frac{1}{r},$$ acting on (a domain contained in) $L^2(\mathbb{R}^3)$. It is …
- 2,358
6
votes
Is zero a hydrogen eigenvalue?
I looked in Anatoly's references, and Quantum mechanics for mathematicians by Leon A. Takhtajan does have the calculation of the continuum wavefunctions, though it does not do the $k=0$ case.
The eige …
- 2,358
3
votes
1
answer
223
views
Analytic continuation of instantaneous eigenstates of a time-dependent hamiltonian
We are considering the instantaneous eigenstates of an analytically time-dependent hamiltonian and I would like to know how legitimate it is to extend them to the complex plane.
Specifically, our ham …
- 2,358
2
votes
0
answers
146
views
Subspace where an operator is positive
Given a self-adjoint operator $\hat{T}$ on a Hilbert space $\mathcal{H}$, and assuming it has a basis of eigenvectors $\{\phi_n\}$ such that $\hat{T}\phi_n=\lambda_n\phi_n$, one can consider the subsp …
- 2,358