摘要
Starting from a time operator, the form of the so called energy operator that is conjugate to the time operator is derived in time representation by analyzing the properties of time translation. This analysis also establishes the commutator between the time and the energy operators. It is seen from the analysis that the energy operator has nothing to do conceptually with the Hamiltonian operator of a system, so that the time operator is not conjugate to the Hamiltonian. Furthermore, it is shown that the Hermiticity of the energy operator requires introducing time integrate inner product. The time energy commutator and the time integral inner product put the time energy uncertainty relation on the same footing as the position momentum uncertainty relation.
Starting from a time operator, the form of the so called energy operator that is conjugate to the time operator is derived in time representation by analyzing the properties of time translation. This analysis also establishes the commutator between the time and the energy operators. It is seen from the analysis that the energy operator has nothing to do conceptually with the Hamiltonian operator of a system, so that the time operator is not conjugate to the Hamiltonian. Furthermore, it is shown that the Hermiticity of the energy operator requires introducing time integrate inner product. The time energy commutator and the time integral inner product put the time energy uncertainty relation on the same footing as the position momentum uncertainty relation.
