Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Schr\"odinger equations with time-dependent potentials growing
  polynomially in the spatial direction   The Cauchy problem for the Schr\"odinger equations is studied with
time-dependent potentials growing polynomially in the spatial direction. First
the existence and the uniqueness of solutions are shown in the weighted Sobolev
spaces. In addition, we suppose that our potentials are depending on a
parameter. Secondly it is shown that if potentials depend continuously and
differentiably on the parameter, the solutions to the Schr\"odinger equations
respectively become continuous and differentiable with respect to its
parameter.

32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom