Open AccessRIGOROUS EVOLVING STATES OF EXP-SIN TYPE FOR THE GENERALIZED TIME-DEPENDENT QUANTUM OSCILLATOR WITH A MOVING BOUNDARY
Author(s) -
Bo-Zang Li,
Ling Li
Publication year - 2001
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.50.1654
Subject(s) - hamiltonian (control theory) , physics , quantum , generality , type (biology) , homogeneous , quadratic equation , boundary value problem , ordinary differential equation , quantum mechanics , mathematics , classical mechanics , mathematical physics , differential equation , statistical physics , geometry , psychology , mathematical optimization , ecology , psychotherapist , biology
In this paper the generalized time-dependent quantum oscillator with a moving boundary is studied. Its Hamiltonian is of the non-homogeneous quadratic form of space-coordinate and momentum with time-dependent coefficients. We obtain an orthonormalized and complete set of rigorous evolving states of Exp-Sin type, as well as the necessary and sufficient condition for the existence of states of this type. Our results are of considerable generality, including as particular cases almost all the results given in literature. In addition, a misunderstanding of a few authors on the differential with respect to time is clarified and we point out that the differentiation with respect to either time or space-coordinate can be performed in the ordinary sense.