Skew-Hermitian operators:

Determine the properties of the eigenvalues and eigenvectors of a skew-Hermitian operator. Are the eigenvalues real, complex, purely imaginary? Are the eigenvectors orthogonal?

Heisenberg uncertainty principle:

Derive the Heisenberg uncertainty principle for the following cases:

a) A and B operators are Hermitian but the quantum state is mixed (not pure)

b) A is Hermitian and and B is skew-Hermitian, the quantum state is pure.

What if A and B are both skew-Hermitian?

**Subject Physics Quantum Physics**