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?