Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge invariant grid discretization of Schr\"odinger equation   Using the Wilson formulation of lattice gauge theories, a gauge invariant
grid discretization of a one-particle Hamiltonian in the presence of an
external electromagnetic field is proposed. This Hamiltonian is compared both
with that obtained by a straightforward discretization of the continuous
Hamiltonian by means of balanced difference methods, and with a tight-binding
Hamiltonian. The proposed Hamiltonian and the balanced difference one are used
to compute the energy spectrum of a charged particle in a two-dimensional
parabolic potential in the presence of a perpendicular, constant magnetic
field. With this example we point out how a "naive" discretization gives rise
to an explicit breaking of the gauge invariance and to large errors in the
computed eigenvalues and corresponding probability densities; in particular,
the error on the eigenfunctions may lead to very poor estimates of the mean
values of some relevant physical quantities on the corresponding states. On the
contrary, the proposed discretized Hamiltonian allows a reliable computation of
both the energy spectrum and the probability densities.

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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph