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Homework Statement
Let A be a Hermitian matrix and consider the matrix U = exp[-iA] defined by thr Taylor expansion of the exponential.
a) Show that the eigenvectors of A are eigenvectors of U. If the eigenvalues of A are a subscript(i) for i=1,...N, show that the eigenvalues of U are exp[-i*a subscript(i)].
b) Show that U is unitary.
This example is important in quantum mechanics when A=Ht/h, where H is the Hamiltonian operator, t is time, and h is Plank's constant. Then U evolves the wavefunction over a time t.
Homework Equations
I have uploaded what I have come up with so far, but not sure where to go with it
The Attempt at a Solution
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See uploaded file