Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

Ling Li, Bo‐Zang Li

Tae Jun Park

Increasing theoretical attention has been paid to solving exactly time-dependent quantum mechanical problems for their own mathematical interest and for applications.Among

Debraj Nath, Amlan K. Roy

Chi‐Fai Lo

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well.

M Liang, B Yuan, Kai Zhong

Under a new quantization scheme, the exact wave functions of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency are obtained. The wave functions are shape-unchanging wave packet with the center moving along the classical trajectory. The total phase of the wave function is explicitly expressed as the sum of the dynamical phase and the geometrical phase. PACS Nos.: 03.65-w, 05.40-a

D. Martínez-Tibaduiza, Luís Barbosa Pires, Daniela Szilard +3 more