2. Determine whether the following operators are linear or nonlinear: (McQuarrie 3-2) a. Âf(x) = SQRF(x) [square f(x)] b. Âf(x) = f'(x) c. Ât(x) = 0 d. Âf(x) = [f(x)]' e. Âf(x) = f(0) f. Ât(x) = Inf(x) [form the complex conjugate of f(x)] [multiply f(x) by zero] [take the reciprocal of f(x)] [evaluate f(x) at x=0] [take the logarithm of f(x)] %3D %3D %3D
2. Determine whether the following operators are linear or nonlinear: (McQuarrie 3-2) a. Âf(x) = SQRF(x) [square f(x)] b. Âf(x) = f'(x) c. Ât(x) = 0 d. Âf(x) = [f(x)]' e. Âf(x) = f(0) f. Ât(x) = Inf(x) [form the complex conjugate of f(x)] [multiply f(x) by zero] [take the reciprocal of f(x)] [evaluate f(x) at x=0] [take the logarithm of f(x)] %3D %3D %3D
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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Question
Pls answer no. 2
![1. Evaluate g = Âf, where  and f are given below: (McQuarrie 3-1)
Â
SQRT (V)
f
(a)
(b)
x4
+ x3
dx'
eax
(c)
dx
x - 2x + 3
(d)
Əx? * ay2
2. Determine whether the following operators are linear or nonlinear: (McQuarrie 3-2)
a. Āf(x) = SQRF(x) [square f(x)]
b. Âf(x) = f'(x)
c. Âf(x) = 0
d. Âf(x) = [f(x)]*1
e. Âf(x) = f(0)
Ât(x) = Inf(x)
[form the complex conjugate of f(x)]
[multiply f(x) by zero]
[take the reciprocal of f(x)]
[evaluate f(x) at x=0]
[take the logarithm of f(x)]
f.
3. In each case, show that f (x) is an eigenfunction of the operator given. Find the eigenvalue.
(McQuarrie 3-3)
f(x)
(а)
d?
coSWX
dx2
d
(b)
e lwt
dt
(c)
eax
+ 3
(d)
ay
4. Determine whether or not the following pairs of operators commute. (McQuarrie 3-6)
(a)
d.
+
dx2
2
dx
(b)
X
dx.
SQRT
(c)
(d)
SQR
Əx
ду
5.
Show that
<X>
for all states of a particle in a box. Is this result physically reasonable? (McQuarrie 3-15)
6. Calculate <x> and <x?> for the n = 2 state of a particle in a one-dimensional box of length a. Show
that:
(McQuarrie 3-26)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2510f38f-6083-499b-ba40-32d6755c47aa%2F097ecf9e-f99c-448b-986e-902deb9c0fdf%2Fmbsugjw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Evaluate g = Âf, where  and f are given below: (McQuarrie 3-1)
Â
SQRT (V)
f
(a)
(b)
x4
+ x3
dx'
eax
(c)
dx
x - 2x + 3
(d)
Əx? * ay2
2. Determine whether the following operators are linear or nonlinear: (McQuarrie 3-2)
a. Āf(x) = SQRF(x) [square f(x)]
b. Âf(x) = f'(x)
c. Âf(x) = 0
d. Âf(x) = [f(x)]*1
e. Âf(x) = f(0)
Ât(x) = Inf(x)
[form the complex conjugate of f(x)]
[multiply f(x) by zero]
[take the reciprocal of f(x)]
[evaluate f(x) at x=0]
[take the logarithm of f(x)]
f.
3. In each case, show that f (x) is an eigenfunction of the operator given. Find the eigenvalue.
(McQuarrie 3-3)
f(x)
(а)
d?
coSWX
dx2
d
(b)
e lwt
dt
(c)
eax
+ 3
(d)
ay
4. Determine whether or not the following pairs of operators commute. (McQuarrie 3-6)
(a)
d.
+
dx2
2
dx
(b)
X
dx.
SQRT
(c)
(d)
SQR
Əx
ду
5.
Show that
<X>
for all states of a particle in a box. Is this result physically reasonable? (McQuarrie 3-15)
6. Calculate <x> and <x?> for the n = 2 state of a particle in a one-dimensional box of length a. Show
that:
(McQuarrie 3-26)
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