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Wavefunctions 3/2 1 (1s) = ,-Zrlao do 3/2 1 4 (2s) 2 4V27 \do.

Wavefunctions 3/2 1 (1s) = ,-Zrlao do 3/2 1 4 (2s) 2 4V27 \do.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that the Hydrogenic Wavefunctions in Table 11.2 obey the Schrodinger Equation

 

TABLE 11.2 Hydrogenic Wavefunctions* n m, 3/2 1 p(1s) : 1 -Zrlao e V\ao. 3/2 1 4 (2s) Zr 2 -Zr/2ao e %3D - 4V2\ao. do 5/2 1 -Zr/2ao 2 1 Y(2p;) (z) e 4V2\ao. Z 5/2 (х) е Zr/2a 1 Y(2px) 4V27\4o. 2 1 土1 Z 5/2 (y) e¯Zr/2ao V(2p,) 4V27 \do. = r cos 0 ao = Bohr radius 0.529 Å = 0.529×1010 m me? x = r sin 0 cos o y = r sin 0 sin & 12 = x? + y? + z? Note that the wavefunctions are separable, such that ¼(r,0,4) = g(r)h(0,4). Z= charge on nucleus %3D || ||
Transcribed Image Text:TABLE 11.2 Hydrogenic Wavefunctions* n m, 3/2 1 p(1s) : 1 -Zrlao e V\ao. 3/2 1 4 (2s) Zr 2 -Zr/2ao e %3D - 4V2\ao. do 5/2 1 -Zr/2ao 2 1 Y(2p;) (z) e 4V2\ao. Z 5/2 (х) е Zr/2a 1 Y(2px) 4V27\4o. 2 1 土1 Z 5/2 (y) e¯Zr/2ao V(2p,) 4V27 \do. = r cos 0 ao = Bohr radius 0.529 Å = 0.529×1010 m me? x = r sin 0 cos o y = r sin 0 sin & 12 = x? + y? + z? Note that the wavefunctions are separable, such that ¼(r,0,4) = g(r)h(0,4). Z= charge on nucleus %3D || ||
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