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The problem of a spin-$\frac{1}{2}$ particle moving in a linear potentialfield in two-dimensions is searched to obtain for nonzero energy eigenvaluesand the corresponding normalized eigenfunctions. The zero-mode ($E=0$)eigenfunctions are also studied and it is seen that they are normalizable. Thevariation of the non-zero eigenfunctions and also eigenvalues are according tothe position and potential parameter $\gamma$, respectively, given in the text.

Exact Solution of a Spin-$\frac{1}{2}$ Particle for a Linear Potential