A Class of Exactly-Solvable Eigenvalue Problems

Carl M. Bender, Qinghai Wang

The class of differential-equation eigenvalue problems $-y^{\prime \prime }(x)+x^{2N+2}y(x)=x^{N}Ey(x)$ ($N=-1,0,1,2,3,...$) on the interval $-\infty <x<\infty$ can be solved in closed form for all…