Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Converting translation operators into plane polar and spherical
  coordinates and their use in determining quantum-mechanical wavefunctions in
  a representation-independent fashion   Quantum mechanics is often developed in the position representation, but this
is not necessary, and one can perform calculations in a
representation-independent fashion, even for wavefunctions. In this work, we
illustrate how one can determine wavefunctions, aside from normalization, using
only operators and how those operators act on state vectors. To do this in
plane polar and spherical coordinates requires one to convert the translation
operator into those coordinates. As examples of this approach, we illustrate
the solution of the Coulomb problem in two and three dimensions without needing
to express any operators in position space.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio