Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy Estimates for Low Regularity Bilinear Schr\"odinger Equations   This paper presents an energy estimate in terms of the total variation of the
control for bilinear infinite dimensional quantum systems with unbounded
potentials. These estimates allow a rigorous construction of propagators
associated with controls of bounded variation. Moreover, upper bounds of the
error made when replacing the infinite dimensional system by its finite
dimensional Galerkin approximations is presented.

8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th