Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quality of Variational Trial States   Besides perturbation theory (which clearly requires the knowledge of the
exact unperturbed solution), variational techniques represent the main tool for
any investigation of the eigenvalue problem of some semibounded operator H in
quantum theory. For a reasonable choice of the employed trial subspace of the
domain of H, the lowest eigenvalues of H usually can be located with acceptable
precision whereas the trial-subspace vectors corresponding to these eigenvalues
approximate, in general, the exact eigenstates of H with much less accuracy.
Accordingly, various measures for the accuracy of the approximate eigenstates
derived by variational techniques are scrutinized. In particular, the matrix
elements of the commutator of the operator H and (suitably chosen) different
operators with respect to degenerate approximate eigenstates of H obtained by
variational methods are proposed as new criteria for the accuracy of
variational eigenstates. These considerations are applied to precisely that
Hamiltonian for which the eigenvalue problem defines the well-known spinless
Salpeter equation. This bound-state wave equation may be regarded as (the most
straightforward) relativistic generalization of the usual nonrelativistic
Schroedinger formalism, and is frequently used to describe, e.g., spin-averaged
mass spectra of bound states of quarks.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas