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In this article, we consider the operator $L$ defined by the differential expression $$\ell \left(y\right)=-y^{\text{'}\text{'}}+q\left(x\right)y,-\infty <x<\infty$$ in $L_2(-\infty ,\infty )$, where $q$ is a complex valued function. Discussing the spectrum, we prove that $L$ has a finite number of eigenvalues and spectral singularities, if the condition $$\underset{-\infty <x<\infty }{sup}\left\{exp\left(ϵ\sqrt{\left|x\right|}\right)\left|q\left(x\right)\right|\right\}<\infty ,ϵ>0$$ holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.