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Wave Mechanics & Angular Momentum question bank (Quantum Mechanics & Statistical Physics)

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Q1.

[Quantum Mechanics & Statistical Physics Problem #2] 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)

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

(B)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

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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)

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

(B)

All eigenvalues are pure imaginary

(C)

Eigenvalues must always be positive integers

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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