Show that Lˆ is a linear operator, i.e., that is satisfies the necessary requirement for linear operators. b) Find Lˆ† and using this find the conditions on k that make Lˆ self-adjoint. c) Find two sets of boundary conditions under which Lˆ is Hermitian

Show that Lˆ is a linear operator, i.e., that is satisfies the necessary requirement for linear operators. b) Find Lˆ† and using this find the conditions on k that make Lˆ self-adjoint. c) Find two sets of boundary conditions under which Lˆ is Hermitian

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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Question

Show that Lˆ is a linear operator, i.e., that is satisfies the necessary requirement for linear
operators.

b) Find Lˆ† and using this find the conditions on k that make Lˆ self-adjoint.

c) Find two sets of boundary conditions under which Lˆ 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*(x)g(x)dx.

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