Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The functional-analytic versus the functional-integral approach to
  quantum Hamiltonians: The one-dimensional hydrogen atom.   The capabilities of the functional-analytic and of the functional-integral
approach for the construction of the Hamiltonian as a self-adjoint operator on
Hilbert space are compared in the context of non-relativistic quantum
mechanics. Differences are worked out by taking the one-dimensional hydrogen
atom as an example, that is, a point mass on the Euclidean line subjected to
the inverse-distance potential. This particular choice is made with the intent
to clarify a long-lasting discussion about its spectral properties. In fact,
for the four-parameter family of possible Hamiltonians the corresponding
energy-dependent Green functions are derived in closed form. The multiplicity
of Hamiltonians should be kept in mind when modelling certain experimental
situations as, for instance, in quantum wires.

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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn