Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Canonical Transformations and the Hamilton-Jacobi Theory in
  Quantum Mechanics   We investigate two methods of constructing a solution of the Schr\"{o}dinger
equation from the canonical transformation in classical mechanics. One method
shows that we can formulate the solution of the Schr\"{o}dinger equation from
linear canonical transformations, the other focuses on the generating function
which satisfies the Hamilton-Jacobi equation in classical mechanics. We also
show that these two methods lead to the same solution of the Schr\"{o}dinger
equation.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con