Example 9.1 (Charged oscillator in an electric field)
A particle of charge ( q ) and mass ( m ), which is moving in a one-dimensional harmonic potential of frequency ( omega ), is subject to a weak electric field ( mathcal{E} ) in the ( x )-direction.
(a) Find the exact expression for the energy.
(b) Calculate the energy to first nonzero correction and compare it with the exact result obtained in (a).
