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If two operators act on a wave function as indicated by  ƒ (x), it is important to carry out the operations in suc cession with the first operation being that nearest to the func tion. Mathematically, ƒ(x) = Â(ƒ(x)) and ²ƒ(x) = Â(ƒ(x)). Evaluate the following successive operations ƒ(x). The operators A and B are listed in the first two columns and f(x) is listed in the third column. Ye-2y³ a. d dy b. y c. y d əx ə d. x- y ду d dy X a y ду ə e-2(x+y) Are your answers to parts (a) and (b) identical? Are your answers to parts (c) and (d) identical? As we will learn in Chapter 17, switching the order of the operators can change the outcome of the operation AB f(x). ye-2y³ əx e-2(x+y)

If two operators act on a wave function as indicated by  ƒ (x), it is important to carry out the operations in suc cession with the first operation being that nearest to the func tion. Mathematically, ƒ(x) = Â(ƒ(x)) and ²ƒ(x) = Â(ƒ(x)). Evaluate the following successive operations ƒ(x). The operators A and B are listed in the first two columns and f(x) is listed in the third column. Ye-2y³ a. d dy b. y c. y d əx ə d. x- y ду d dy X a y ду ə e-2(x+y) Are your answers to parts (a) and (b) identical? Are your answers to parts (c) and (d) identical? As we will learn in Chapter 17, switching the order of the operators can change the outcome of the operation AB f(x). ye-2y³ əx e-2(x+y)

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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P13.4 If two operators act on a wave function as indicated by AB f(x), it is important to carry out the operations in suc- cession with the first operation being that nearest to the func- tion. Mathematically, ƒ(x) = Â(ƒ(x)) and ²ƒ(x) = Â(ƒ(x)). Evaluate the following successive operations ƒ(x). The operators A and B are listed in the first two columns and f(x) is listed in the third column. Ye-2y³ a. d dy b. y c. y ə d. x əx a y ду d dy X ə y ду ə e-2(x+y) Are your answers to parts (a) and (b) identical? Are your answers to parts (c) and (d) identical? As we will learn in Chapter 17, switching the order of the operators can change the outcome of the operation  ƒ(x). Ye-2y,³ əx e-2(x+y)
Transcribed Image Text:P13.4 If two operators act on a wave function as indicated by AB f(x), it is important to carry out the operations in suc- cession with the first operation being that nearest to the func- tion. Mathematically, ƒ(x) = Â(ƒ(x)) and ²ƒ(x) = Â(ƒ(x)). Evaluate the following successive operations ƒ(x). The operators A and B are listed in the first two columns and f(x) is listed in the third column. Ye-2y³ a. d dy b. y c. y ə d. x əx a y ду d dy X ə y ду ə e-2(x+y) Are your answers to parts (a) and (b) identical? Are your answers to parts (c) and (d) identical? As we will learn in Chapter 17, switching the order of the operators can change the outcome of the operation  ƒ(x). Ye-2y,³ əx e-2(x+y)
Expert Solution
Step 1

Given:

  A^ B^ fx
a. ddy y ye-2y3
b. y ddy ye-2y3
c. y∂∂x x∂∂y e-2x+y
d. x∂∂y y∂∂x e-2x+y

We have to evaluate: A^B^fx

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