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--- hamburgminicourse2017:stone_s_theorem [2017/04/02 15:23] – markus
+++ hamburgminicourse2017:stone_s_theorem [2017/04/02 15:26] (current) – markus
@@ Line 31: / Line 31: @@
 \]
-Stone's theorem can also be taken as a one-to-one correspondence between self-adjoint operators and unitary one-parameter groups. For any given unitary one-parameter group on a Hilbert space there exists a unique self-adjoint generator in the role of the Hamiltonian. This operator is then defined as a limit as [[the_abstract_cauchy_problem_in_banach_space|before]] that does not necessarily converge for all $\psi \in \H$ which gives the respective domain of the Hamiltonian.
+Stone's theorem can also be taken as a one-to-one correspondence between self-adjoint operators and unitary one-parameter groups. For any given unitary one-parameter group on a Hilbert space there exists a unique self-adjoint generator in the role of the Hamiltonian. This operator is then defined as a limit as [[the_abstract_cauchy_problem_in_banach_space|before]] that does not necessarily converge for all $\psi \in \mathcal{H}$ which gives the respective domain of the Hamiltonian.
 \[
 H\psi = \lim_{t \rightarrow 0} \frac{\exp(-i H t)\psi - \psi}{t}
@@ Line 41: / Line 41: @@
 \exp(-i H t) = \int \exp(-i \varepsilon t) \,d E_{H}(\varepsilon)
 \]
+ >> [[Classes of static potentials]]