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Function space requirements for the single-electron functions within the multiparticle Schrödinger equation
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10.1063/1.4811396
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1 Department of Mathematics, Ohio University, Athens, Ohio 45701, USA
J. Math. Phys. 54, 062105 (2013)
/content/aip/journal/jmp/54/6/10.1063/1.4811396
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/6/10.1063/1.4811396

## Figures

FIG. 1.

For = 1 and = 3, the radial part of φ() (upper left), 4π|φ()| (upper right), 4π|φ()| (lower left), and 4π|φ()| (lower right) for 0 ⩽ ⩽ 2. The latter three illustrate the concentration of the , , and norms, respectively.

FIG. 2.

The bound on (vertical axis) as a function of (horizontal axis, [3.1, 13]) using the bound and assuming only φ ∈ . The bound becomes infinite at = 3.

FIG. 3.

The sharpness bound on (vertical axis) as a function of the (horizontal axis, [3.1, 23]) used for , which assumes only φ ∈ . The bounds become infinite at = 3 and go to values less than 3 as → ∞.

FIG. 4.

The bound on (vertical axis) as a function of (horizontal axis) using = 5 and three values for in .

FIG. 5.

The bound on (vertical axis) for = 2 (left plot) and = (right plot) as a function of the (horizontal axis) used for for a selection of used for .

FIG. 6.

The bound on (vertical axis) for = 2 and = as a function of the (horizontal axis; [3.1, 50]) used for .

FIG. 7.

The bound on (vertical axis) as a function of (horizontal axis) for a selection of used for ‖φ‖.

## Tables

Table I.

Sharpness factors for various bounds.

Table II.

Maximum amplification of terms due to linear combinations using core orbital sizes and −μ ∼ , neglecting constants.

Table III.

Modified amplification of terms.

/content/aip/journal/jmp/54/6/10.1063/1.4811396
2013-06-24
2014-04-16

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