Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On form-preserving transformations for the time-dependent Schr\"odinger
  equation   In this paper we point out a close connection between the Darboux
transformation and the group of point transformations which preserve the form
of the time-dependent Schr\"odinger equation (TDSE). In our main result, we
prove that any pair of time-dependent real potentials related by a Darboux
transformation for the TDSE may be transformed by a suitable point
transformation into a pair of time-independent potentials related by a usual
Darboux transformation for the stationary Schr\"odinger equation. Thus, any
(real) potential solvable via a time-dependent Darboux transformation can
alternatively be solved by applying an appropriate form-preserving
transformation of the TDSE to a time-independent potential. The preeminent role
of the latter type of transformations in the solution of the TDSE is
illustrated with a family of quasi-exactly solvable time-dependent anharmonic
potentials.

33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph