Quantum theory of a free electron in a tapered wiggler field

It is pointed out that a slight modification of the relativistic quantum theory of a free electron in a uniform wiggler field enables the study of motion in a tapered wiggler field of the form $\text{k}{}_{\mathrm{w}}{}^1\text{= k}{}_{\mathrm{w}}\text{?}\text{b}\text{z}$ which merits attention. The lower limit of z is 800 cm. The exact relativistic quantum mechanical calculation shows an enhancement in the gain for single pass. The frequencies are up-shifted by amounts depending on the parameter b.