Abstract:
An algebraic apparatus based on increasing $B_p^+$ and decreasing $B_{p}$ operators $(p=2,3,\ldots,N)$ is developed to solve the one-dimensional model of N interacting particles studied
by Calogero [J. Math. Phys., 10, 2191, 2197 (1969)]. The determination of the wave functions
of the Schrödinger equation is then reduced to the operation of differentiation. Explicit
expressions are obtained for the operators $B_{p}$ and $B_p^+$ for $p=2,3,$ and 4. All the wave functions
for the case of four particles can be found by means of these expressions. For an arbitrary
number of particles this then yields an expression for two new series of wave functions
that depend on three quantum numbers. The operators of higher order can be found by
the same method
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