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Results tagged with sp.spectral-theory
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user 109757
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
2
votes
1
answer
130
views
Pseudo-polynomial potentials for Schrödinger operators
Consider the one dimensional Schrödinger hamiltonian $\mathcal{H}=-\frac{\hbar^2}{2} \frac{d^2}{dx^2} + V(x)$.
Suppose that $V:\mathbb{R} \rightarrow \mathbb{R}^+$ is a continuous and confining poten …
- 129
6
votes
2
answers
519
views
Schrödinger eigenfunctions are bounded
Let $V:\mathbb{R}\rightarrow \mathbb{R}^{+ *}$ a real positive function such that $\displaystyle \lim_{ x \to \pm\infty} V(x)= +\infty $.
Then the Schrödinger operator $H=-\frac{d^2}{dx^2}+V(x)$ has …
- 129
1
vote
2
answers
216
views
Ground state has always constant sign?
Question: What hypothesis on the potential $V$ are required such that the ground state $\phi_0$ has constant sign?
Consider the Schrödinger operator in 1 dimension with potential $V$:
$$\mathcal{H}= …
- 129