Consider the following Hamiltonians whose matrix forms are as follows a) Find the eigenvalues and eigenfunctions of Hˆ1 and Hˆ2. Are they degenerate? b) Find the non-trivial conditions on a, b and c for Hˆ1 to be Hermitian and Hˆ2 to be Hermitian?

Consider the following Hamiltonians whose matrix forms are as follows a) Find the eigenvalues and eigenfunctions of Hˆ1 and Hˆ2. Are they degenerate? b) Find the non-trivial conditions on a, b and c for Hˆ1 to be Hermitian and Hˆ2 to be 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 following Hamiltonians whose matrix forms are as follows

a) Find the eigenvalues and eigenfunctions of Hˆ1 and Hˆ2. Are they degenerate?

b) Find the non-trivial conditions on a, b and c for Hˆ1 to be Hermitian and Hˆ2 to be Hermitian?

H1 = |1) 4 (1| + |1) c (2| + |2) (1 + |2) 6 (2] + |2) a (3| + |3) (–2 +c) (3|
n-()
3
H2
1

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