Physics – Quantum Physics
Scientific paper
2001-02-05
Phys. Rev. A 63, 032104 (2001)
Physics
Quantum Physics
Physical Review A in Press
Scientific paper
10.1103/PhysRevA.63.032104
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of different timescale is found. If the interactions can be written in terms of the differences between positions of two particles, it is also shown that the Schr\"{o}dinger equation is invariant under a unitary transformation. These unitary relations can be used not only in finding coherent states from the given stationary states in a system, but also in finding exact wave functions of the Hamiltonian systems of time-dependent parameters from those of time-independent Hamiltonian systems. Both operators are invariant under the exchange of any pair of particles. The transformations are explicitly applied for some of the Calogero-Sutherland models to find exact coherent states.
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