A time representation

The paper contains a proposal for an energy and time representation. We construct modes that correspond to fuzzy distributions around discrete values of energy or time. The modes form an orthogonal and complete set in the space of square integrable functions. Energy and time are self adjoint in the space spanned by the modes. The widths of the modes are analyzed as well as their energy-time uncertainty relations. The lower uncertainty attainable for the modes is shown. We also show times of arrival for massless particles.