226
Appendix C: The Dirac δ Function and the Normalization of Continuum States
δ(k − k
) = δ
√
2μ
E − U ∞ −
E − U ∞
=
2 2 (E − U ∞ )
μ
δ(E − E
)
(C.16)
The last passage makes use of Eq. (C.7). So, the normalization factor we need is:
N (E) =
2μ
π 2 2 (E − U ∞ )
1/4
(C.17)
References
1. Dennery, P., Krzywicki, A.: Mathematics for Physicists. Dover, Mineola (1995)
2. Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists.
Elsevier, Amsterdam (2012)
Appendix C: The Dirac δ Function and the Normalization of Continuum States
δ(k − k
) = δ
√
2μ
E − U ∞ −
E − U ∞
=
2 2 (E − U ∞ )
μ
δ(E − E
)
(C.16)
The last passage makes use of Eq. (C.7). So, the normalization factor we need is:
N (E) =
2μ
π 2 2 (E − U ∞ )
1/4
(C.17)
References
1. Dennery, P., Krzywicki, A.: Mathematics for Physicists. Dover, Mineola (1995)
2. Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists.
Elsevier, Amsterdam (2012)