2/2 -irT b1 (r)e¬3iwT/2 + Ve-irT 2(r)e-biwT/2 V(x,T) = -irT %3D e 드n(x)e-(r+ ¥)T + 2/2 2(x)e-(r+)7 The aim is to choose r in order to minimize T, which must satisfy exp r+ = 1 exp = -1 exp +. = 1
2/2 -irT b1 (r)e¬3iwT/2 + Ve-irT 2(r)e-biwT/2 V(x,T) = -irT %3D e 드n(x)e-(r+ ¥)T + 2/2 2(x)e-(r+)7 The aim is to choose r in order to minimize T, which must satisfy exp r+ = 1 exp = -1 exp +. = 1
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
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why the equation must satisfy the part that surrounded by block?
![3
V (x, T) =
2/2
-irT
-irT
e
5
-irT
e
/2(r)e-5iwT/2
po (x)e-iwT/2 _
V1 (x)e-3iwT/2
5
2v2 bo(x)e-i(r+)T
2(x)e=i(r+)T
5
3
= vo (x)e-i(r+)T _
1(2)e¬i(r+)T +
The aim is to choose r in order to minimize T, which must satisfy
exp [-(r+ )7] = 1
?
exp
+.
= -1
exp
r+
T = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F622a7a2e-be53-4471-adaf-e7058f6dc381%2Fd8e7cbc6-de99-48be-8994-3090963537b1%2F79kwk9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
V (x, T) =
2/2
-irT
-irT
e
5
-irT
e
/2(r)e-5iwT/2
po (x)e-iwT/2 _
V1 (x)e-3iwT/2
5
2v2 bo(x)e-i(r+)T
2(x)e=i(r+)T
5
3
= vo (x)e-i(r+)T _
1(2)e¬i(r+)T +
The aim is to choose r in order to minimize T, which must satisfy
exp [-(r+ )7] = 1
?
exp
+.
= -1
exp
r+
T = 1
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