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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
/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

Image of FIG. 1.
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.

Image of FIG. 2.
FIG. 2.

The bound on (vertical axis) as a function of (horizontal axis, [3.1, 13]) using the bound (114) and assuming only φ ∈ . The bound becomes infinite at = 3.

Image of FIG. 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 → ∞.

Image of FIG. 4.
FIG. 4.

The bound on (vertical axis) as a function of (horizontal axis) using = 5 and three values for in (118) .

Image of FIG. 5.
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 .

Image of FIG. 6.
FIG. 6.

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

Image of FIG. 7.
FIG. 7.

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

Tables

Generic image for table

Generic image for table
Table I.

Sharpness factors for various bounds.

Generic image for table
Table II.

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

Generic image for table
Table III.

Modified amplification of terms.

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/content/aip/journal/jmp/54/6/10.1063/1.4811396
2013-06-24
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Function space requirements for the single-electron functions within the multiparticle Schrödinger equation
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/6/10.1063/1.4811396
10.1063/1.4811396
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