On the Time Operator in Quantum Mechanics: Three Typical Examples

Abstract

The so-called time operator in quantum mechanics which may be regarded as a coordinate conjugate to Hamiltonian operator is studied. Three typical examples of the time operators in one-dimensional problem are explicitly obtained; that is, a free particle, a harmonic oscillator and a particle in a square well potential. Our procedure to construct the time operator seems to be useful in a more general case. Qualitative nature of the time operator may be understood from the three examples.