Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sum Rule of Quantum Uncertainties: Coupled Harmonic Oscillator System
  with Time-Dependent Parameters   Uncertainties $(\Delta x)^2$ and $(\Delta p)^2$ are analytically derived in
an $N$-coupled harmonic oscillator system when spring and coupling constants
are arbitrarily time-dependent and each oscillator is in an arbitrary excited
state. When $N = 2$, those uncertainties are shown as just arithmetic average
of uncertainties of two single harmonic oscillators. We call this property as
"sum rule of quantum uncertainty". However, this arithmetic average property is
not generally maintained when $N \geq 3$, but it is recovered in $N$-coupled
oscillator systems if and only if $(N-1)$ quantum numbers are equal. The
generalization of our results to a more general quantum system is briefly
discussed.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: stat