Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyers--Ulam stability for quantum equations   We introduce and study the Hyers--Ulam stability (HUS) of a Cayley quantum
($q$-difference) equation of first order, where the constant coefficient is
allowed to range over the complex numbers. In particular, if this coefficient
is non-zero, then the quantum equation has Hyers--Ulam stability for certain
values of the Cayley parameter, and we establish the best (minimal) HUS
constant in terms of the coefficient only, independent of $q$ and the Cayley
parameter. If the Cayley parameter equals one half, then there is no
Hyers--Ulam stability for any coefficient value in the complex plane.

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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex