# Tagged Questions

The tag has no usage guidance.

60 views

227 views

### Travelling waves for nonlinear Schrödinger equation

Consider the following nonlinear Schrödinger equation: $$-\Delta \Phi - i\frac{\partial \Phi}{\partial t} = f(|\Phi|^2)\Phi,$$ where $\Delta$ is the Laplacian on $\mathbb{R}^n$, $f$ gives the ...
164 views

131 views

### Decay of Eigenfunctions for the 1D Discrete Random Schrodinger Operators

Consider the operator on $\ell^2(\mathbb{Z})$ $$H = \Delta + v.$$ Here $\Delta$ is the nearest neighbour Laplacian on $\mathbb{Z}$, $\Delta_{k, \ell} =1$ if $|k - \ell| =1$ and zero otherwise, ...
209 views

### Asymptotic behavior of Schrödinger operators

I am currently dealing with $1$ or at most $2$-dimensional Schrödinger operators on compact domains. A classical result of spectral theory is the Weyl approximations for this operator $H = -\Delta +V$....
220 views

483 views

### problem related to Airy functions [closed]

I have solved the Schrödinger equation for a triangular well potential and the solution comes in terms of Airy functions...now i am facing the following problems: What are the normalization ...
390 views

### Asymptotic Expansion of the Schrödinger kernel?

My stackexchange post [http://math.stackexchange.com/questions/275830/schrodinger-kernels-on-manifolds] was somewhat unsatisfactory (also because I may not have stated clear enough what my interest ...
494 views

### Resonance of Schrödinger operator

Consider the dispersive estimates for the Schrödinger flow $$e^{itH}P_{c},\quad H=-\Delta+V \quad \text{on}\quad \mathbb{R}^n,n\ge 1$$ where $P_{c}$ is the projection onto the continuous spectrum ...
75 views

### Random Schrödinger operators with asymmetric Lifshitz tails?

For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
451 views

### First eigenvalue of Schrödinger operator is simple

I once read that the first eigenvalue of a Schrödinger operator always is simple, together with an easy proof of it. But I cannot remember where. Does anybody know a reference?
341 views

### Semiclassical expansions of eigenvalues of Schrödinger operators

Considering Schrödinger operators $$H(\hbar) = \hbar \Delta + V$$ where $V$ is some potential, perturbation theory tells that the eigenvalues of $H(\hbar)$ are holomorphic on some region containing ...
Consider the Schrödinger operator $H_\hbar = -\hbar^2\Delta + V$ on $M=\mathbb{R}^n$, where $V$ is a potential that behaves well in a certain sense ($C^\infty$, bounded from below, going to infinity ...
Manin ends his 1978 ICM talk with this remark: I would also like to mention I. M. Gel'fand's suggestion that the $\zeta$-functions of certain special differential operators should have an arithmetic ...