Show that the Hydrogenic Wavefunctions in Table 11.2 obey the Schrodinger Equation TABLE 11.2 Hydrogenic Wavefunctions*nm,3/21p(1s) :1-ZrlaoeV\ao.3/214 (2s)Zr2-Zr/2aoe%3D-4V2\ao.do5/21-Zr/2ao21Y(2p;)(z) e4V2\ao.Z 5/2(х) е Zr/2a1Y(2px)4V27\4o.21土1Z 5/2(y) e¯Zr/2aoV(2p,)4V27 \do.= r cos 0ao =Bohr radius0.529 Å= 0.529×1010 mme?x = r sin 0 cos oy = 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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Description: Show that the Hydrogenic Wavefunctions in Table 11.2 obey the Schrodinger Equation TABLE 11.2 Hydrogenic Wavefunctions*nm,3/21p(1s) :1-ZrlaoeV\ao.3/214 (2s)Zr2-Zr/2aoe%3D-4V2\ao.do5/21-Zr/2ao21Y(2p;)(z) e4V2\ao.Z 5/2(х) е Zr/2a1Y(2px)4V27\4o.21土1Z 5/

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

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
||
||

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