Introduction

Recent interest in ladder operators [#!Fitts!#], and the curious omission from all current texts of the ladder operator solution to the particle in a box problem of elementary quantum mechanics makes one suspect that hidden in notes in various laboratories scattered all over the world are the details of why this particular approach, when applied to this particular problem, is not particularly pedagogically valid.

Were it otherwise, it would imply that no one has thought of applying this wonderful technique to what is the simplest of all quantum mechanical problems. Since it is inconceivable that persons teaching the ladder operator technique for harmonic oscillators [#!Montemayor!#], rigid rotors and angular momentum [#!LangeRaab2!#,#!LangeRaab3!#], and the H-atom [#!Newmarch!#,#!Boyling!#,#!David!#], etc., have not thought of this application, it must be that there is something curious about the problem that makes it of less than paramount interest.

Here is an approach to the ladder operator problem for the particle in a box in the domain $0 \le x \le L$ which possibly illustrates why the method has not gained universal acceptance for this problem. It appears to be related to that of Kais and Levine [#!KaisLevine!#].