Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superintegrable and shape invariant systems with position dependent mass   Second order integrals of motion for 3d quantum mechanical systems with
position dependent masses (PDM) are classified. Namely, all PDM systems are
specified which, in addition to their rotation invariance, admit at least one
second order integral of motion. All such systems appear to be also shape
invariant and exactly solvable. Moreover, some of them possess the property of
double shape invariance and can be solved using two different superpotentials.
Among them there are systems with double shape invariance which present nice
bridges between the Coulomb and isotropic oscillator systems.
  A simple algorithm for calculation the discrete spectrum and the
corresponding state vectors for the considered PDM systems is presented and
applied to solve five of the found systems.

31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph