Given some $\|\psi \|$ $\in$ $L^2 (\mathbb R^n) $ such that $\| \psi \|_2 =1$ and a function (potential) $V: \mathbb R^n \rightarrow \mathbb R$. The Schorödinger equation tells us that $-\triangle ...
A book on Quantum Mechanics by Schwinger states, "A unitary operator can be considered to be a complex valued function of a Hermitian operator." Please give a hint on how to prove this assertion.
I am looking for an operator $U$, that can do this to a function: $$Uf(x)=f(2x).$$ In particular I am happy if there is an $U$ for the general case: $Uf(x)=f(kx)$. Does such an operator exist for ...