IIT JAM & CSIR NET - Physical Sciences

Condensed Matter Physics question bank (Solid State Physics & Electronics)

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Q1.

[Solid State Physics & Electronics 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)

All eigenvalues are pure imaginary

(C)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

[Solid State Physics & Electronics Problem #4] Regarding Cauchy-Riemann equations for an analytic function f(z) = u(x,y) + i v(x,y): Which of the following analytical formulations is correct?

(A)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(B)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(D)

∂u/∂x + ∂v/∂y = 0 and ∂u/∂y + ∂v/∂x = 0

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