For some systems, the potential energy is some function of a coordinate. For example, the potential
energy of an electron bound to the nucleus of a hydrogen atom is given by e
2 / r , where e is the charge
on the electron and r is a coordinate. Therefore, when this potential function is placed in operator
form, it is the same as in classical form, e
2 / r (see Table 2.1).
In order to put the kinetic energy in operator form, we make use of the fact that the kinetic energy can
be written in terms of the momentum as