IIT JAM & CSIR NET - Physical Sciences

Statistical Mechanics & Ensembles question bank (Quantum Mechanics & Statistical Physics)

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Q1.
[Quantum Mechanics & Statistical Physics Problem #2] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
Eigenvalues must always be positive integers
(B)
The matrix cannot be diagonalized under any orthogonal transformation
(C)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(D)
All eigenvalues are pure imaginary
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Q2.
[Quantum Mechanics & Statistical Physics Problem #4] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
Eigenvalues must always be positive integers
(B)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(C)
The matrix cannot be diagonalized under any orthogonal transformation
(D)
All eigenvalues are pure imaginary
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