OSCILLATORS IN ONE AND 2 DIMENSIONS AND LADDER OPERATORS FOR THE MORSE AND COULOMB PROBLEMS

We exhibit that the radial eigenfunctions of a 2D-harmonic oscillator (2DHO) may be regarded as 1D-harmonic oscillator (1DHO) matrix element s. From this simple fact and using as a starting point the ladder oper ators (a) over cap(+/-) for 1DHO, we obtain ladder operators for 2DHO. Furthermore, by using the relationship between the Coulomb and Morse problems with a 2DHO, we are able to obtain the ladder operators for t he former problems without explicitly recurring to the factorization m ethod. Some uses of the technique presented are suggested. (C) 1997 Jo hn Wiley & Sons, Inc.