3 P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer, New York, 2005), Chap. 9. 4 I. R. Lapidus, “Relativistic one-dimensional hydrogen atom,” Am. J. Phys. 51 , 1036–1038 (1983). 5 N. Bera, K. Bhattacharya, and J. K. Bhattacharjee, “Perturbative and non-perturbative studies with the delta function potential,” Am. J. Phys. 76 , 250–257 (2008). 6 Y. N. Joglekara, “Particle in a box with a δ -function potential: Strong and weak coupling limits,” Am. J. Phys. 77 , 734–736 (2009). 7 E. Schr¨ odinger, “A method of determining quantum-mechanical eigenvalues and eigenfunc- tions,” Proc. Roy. Irish Acad. Sect. A 46 , 9–16 (1941). 8 E. Schr¨ odinger, “Further studies on solving eigenvalue problems by factorization,” Proc. Roy. Irish Acad. Sect. A 46 , 183–206 (1941). 9 E. Schr¨ odinger, “The factorization of the hypergeometric equation,” Proc. Roy. Irish Acad. Sect. A 47 , 53–54 (1941) or arXiv:physics/9910003. 10 P. M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958). 11 I. Infeld and T. E. Hull, “The factorization method,” Rev. Mod. Phys. 23 , 21–68 (1951). 12 H. S. Green, Matrix Methods in Quantum Mechanics (Barnes & Noble, New York, 1968). 13 H. C. Ohanian, Principles of Quantum Mechanics (Prentice Hall, Englewood Cliffs, NJ, 1990). 8