The eigenvalue spectrum in quantum mechanics and the nonlinearization procedure

Ground State of the H3+ Molecular Ion: Physics Behind

“…Our result is slightly worse than one by [37] (6) and (12)(13)(14)(15)(16) . Corresponding results obtained with other methods are displayed for comparison.…”

“…Hence, the above condition underlines the importance of the large-range behavior of the trial functions. In the physics language the above requirement means that the phenomenon of the Dyson's instability should not occur (for a discussion see [15]) 2 .…”

“…Let us recall the essentials of this perturbation theory (for details, see [15][16][17]). Let us assume that the original Hamiltonian has a form H = −∆ + V , where ∆ is the Laplacian.…”

“…the trial function should support the symmetries of the system, has to reproduce the Coulomb singularities and the asymptotic behavior at large distances adequately (see, e.g. [15][16][17]). To the problem finding a bound state of (3p, 2e) giving rise to H + 3 molecular ion we follow the description given in [11].…”

The HeH+molecular ion in a magnetic field

“…The recipe of choice of trial functions is based on physical arguments [15]. A trial function for states with orbital magnetic quantum number m is chosen in the form…”