40 citations · 278 across the 24 of their papers we have counts for
17 papers · 1 filter
Low-lying energy bands in a finite periodic multiple-well potential
Dae-Yup Song
We analyze the low-lying states for a one-dimensional potential consisting of identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave…
Localization or tunneling in asymmetric double-well potentials
Dae-Yup Song
An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrie…
Coherent Control of Tunneling in Double-Well Potentials
Dae-Yup Song
For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each w…
Tunneling and energy splitting in an asymmetric double-well potential
Dae-Yup Song
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency and the difference of the minima is close to a multiple…
Generalization of the Darboux transformation and generalized harmonic oscillators
Dae-Yup Song, John R. Klauder
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the -fold…
Unitary relation for the time-dependent SU(1,1) systems
Dae-Yup Song
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation be…
Harmonic Oscillator, Coherent States, and Feynman Path Integral
Dae-Yup Song
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the o…
Unitary transformation for the system of a particle in a linear potential
Dae-Yup Song
A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely re…
Coherent States and Geometric Phases in Calogero-Sutherland Model
Dae-Yup Song, JeongHyeong Park
Exact coherent states in the Calogero-Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials a…
Exact coherent states in one-dimensional quantum many-body systems with inverse-square interactions
Dae-Yup Song
For the models of -body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent p…
Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential
Dae-Yup Song
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and…
Geometric phases in the simple harmonic and perturbative Mathieu's oscillator systems
JeongHyeong Park, Dae-Yup Song
Geometric phases of simple harmonic oscillator system are studied. Complete sets of "eigenfunctions" are constructed, which depend on the way of choosing classical solutions. For a…
Geometric Phase, Hannay's Angle, and an Exact Action Variable
Dae-Yup Song
Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of co…
Berry phase in the simple harmonic oscillator
JeongHyeong Park, Dae-Yup Song
Berry phase of simple harmonic oscillator is considered in a general representation. It is shown that, Berry phase which depends on the choice of representation can be defined unde…
Periodic Hamiltonian and Berry's phase in harmonic oscillators
Dae-Yup Song
For a time-dependent -periodic harmonic oscillator of two linearly independent homogeneous solutions of classical equation of motion which are bounded all over the time (stable)…
Unitary relations in time-dependent harmonic oscillators
Dae-Yup Song
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscil…
Exact quantum states of a general time-dependent quadratic system from classical action
Dae-Yup Song
A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization wh…