Consider the operator Î=k, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by (f\g) = f* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators. b) Find ι and using this find the conditions on k that make Î self-adjoint. c) Find two sets of boundary conditions under which I is Hermitian.
Consider the operator Î=k, where k is a scalar, operating in a function space on the interval [a, b] with inner product defined by (f\g) = f* f*(x)g(x)dx. a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear operators. b) Find ι and using this find the conditions on k that make Î self-adjoint. c) Find two sets of boundary conditions under which I is Hermitian.
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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![Consider the operator Î=k, where k is a scalar, operating in a function space on the interval
[a, b] with inner product defined by
(f\g) = f* f*(x)g(x)dx.
a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear
operators.
b) Find ι and using this find the conditions on k that make Πself-adjoint.
c)
Find two sets of boundary conditions under which I is Hermitian.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffade91a1-6997-42f9-8725-9969e19df335%2F7c9ae054-b1a5-4e5a-8d20-18f611921075%2F8dfhfwc_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the operator Î=k, where k is a scalar, operating in a function space on the interval
[a, b] with inner product defined by
(f\g) = f* f*(x)g(x)dx.
a) Show that I is a linear operator, i.e., that is satisfies the necessary requirement for linear
operators.
b) Find ι and using this find the conditions on k that make Πself-adjoint.
c)
Find two sets of boundary conditions under which I is Hermitian.
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