2uE F=0 -F = 0 (22) dr2 Note that u, E' and ħ are all positive constants. (f) Using auxiliary equation to solve (22) to show that F = Ae + Be Now we need to apply a boundary condition First we must not allow our solution to contain information about the situation when the particles are free. The particles are free when there is no potential to bound them to each other (i.e. V = + 0). We can see that the potential approaches to 0 when r → 0o. Therefore, the solution must vanish when r 00 Aregr

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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dF 2µE
dr2
-Fx = 0
(22)
Note that u, E' and h are all positive constants.
(f) Using auxiliary equation to solve (22) to show that
= Ae-,
+ Be
Now we need to apply a boundary condition First we must not allow our
solution to contain information about the situation when the particles are
free. The particles are free when there is no potential to bound them to
each other (i.e. V = + 0). We can see that the potential approaches
to 0 when r → 00. Therefore, the solution must vanish when r+ 00
4regr
Transcribed Image Text:dF 2µE dr2 -Fx = 0 (22) Note that u, E' and h are all positive constants. (f) Using auxiliary equation to solve (22) to show that = Ae-, + Be Now we need to apply a boundary condition First we must not allow our solution to contain information about the situation when the particles are free. The particles are free when there is no potential to bound them to each other (i.e. V = + 0). We can see that the potential approaches to 0 when r → 00. Therefore, the solution must vanish when r+ 00 4regr
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