Potential energy as observable

[AlonsoMcLaren]

In quantum mechanics it seems that the operator for potential energy is U. Therefore, every state is an eigenstate of potential energy and there will never be any uncertainty in potential energy? It seems weird...

 

[dextercioby]

The potential energy is only part of the whole Hamiltonian. It can be rendered self-adjoint but typically won't share eigenstates with the whole Hamiltonian, so any 'uncertainty' for it is a meaningless concept.

 

[A. Neumaier]

In quantum mechanics it seems that the operator for potential energy is U. Therefore, every state is an eigenstate of potential energy and there will never be any uncertainty in potential energy? It seems weird...

U is a function of the positions, hence it inherits its uncertainty from these.
(It doesn't matter that U is only part of the Hamiltonian.)