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Look for the expectation value of x, , for a-particle-in-a-box, such that: ηπχ (x) = x xsin² dx €1³

Look for the expectation value of x, , for a-particle-in-a-box, such that: ηπχ (x) = x xsin² dx €1³

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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Look for the expectation value of x, <x>, for a-particle-in-a-box, such that: 2 ηπχ x) = ²/ [²*xsin ² (7x) dx a. a apply these clues in order to arrive at the complete solution and answer: a. Use the identify: sin²x = 2 cos(2x) 2 b. Two transformations of variables: u == in one step and v = 2ânu in another c. Use of integration by parts in finding ſucos(2ânu)du which should come out in one transformation of variables: where ffg' = fg - Sf'g f = u and g' = сos(2лnu)
Transcribed Image Text:Look for the expectation value of x, <x>, for a-particle-in-a-box, such that: 2 ηπχ x) = ²/ [²*xsin ² (7x) dx a. a apply these clues in order to arrive at the complete solution and answer: a. Use the identify: sin²x = 2 cos(2x) 2 b. Two transformations of variables: u == in one step and v = 2ânu in another c. Use of integration by parts in finding ſucos(2ânu)du which should come out in one transformation of variables: where ffg' = fg - Sf'g f = u and g' = сos(2лnu)
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