Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic formula for quantum harmonic oscillator tunneling
  probabilities   Using simple methods of asymptotic analysis it is shown that for a quantum
harmonic oscillator in n-th energy eigenstate the probability of tunneling into
the classically forbidden region obeys an unexpected but simple asymptotic
formula: the leading term is inversely proportional to the cube root of n.

34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio