Ladder operators for isospectral oscillators
摘要
We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the -generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.
关键词
引用
@article{arxiv.quant-ph/9905100,
title = {Ladder operators for isospectral oscillators},
author = {S. Seshadri and V. Balakrishnan and S. Lakshmibala},
journal= {arXiv preprint arXiv:quant-ph/9905100},
year = {2009}
}
备注
13 pages