ar X iv : h ep - p h / 03 12 28 0 v 1 1 9 D ec 2 00 3 Plane waves and wave packets in particle oscillations

Manipulation with ill-defined notions creates an illusion of a simple derivation of the standard phase of neutrino oscillations in hep-ph/0311241 and hep-ph/0312180. Recent remark [1] on a too simple (one page) derivation [2] of the standard formula for neutrino oscillations has been criticized in [3]. Let us remind that the derivation in [2] is based on ”the plane wave approach, in which the massive neutrino states evolve in space and time as plane waves |νk(x, t) >= e kk|νk >”. The plane wave approach describes free particle. This is confirmed by equation E k = p 2 k +m 2 k explicitly written out on the same page in [2]. As is well known, this is the standard definition of the plane wave approach, used e.g. in the description of kaon oscillations. Let us add that ”the plane wave approach” is confronted with ”the wave packet treatment” in the first sentence on the page 3 of ref.[2]. Moreover, in the concluding paragraph of ref.[3] it is stressed that the plane wave approach presented in ref.[2] ”is rather attractive because it is simple, avoiding wave packet complications, and uses a minimum of well-motivated assumptions”. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]