Several properties of Bose-Einstein condensed atoms confined in a double well potential (DWP) are investigated, which include the tunneling effect, interfer- ence of the condensed atoms and the dynamics of the atom-standing wave laser field system.

For both the quartic-anharmonics and double well potentials.

A new kind of double-well potential is studied, which is smoothly joined by three piecewise potentials with the form 1/2kx2 (k∈R) in one-dimension.

We exactly solved two kinds of potentials constructed by this method,one is a double-well potential and adother is a periodic one,both of them are smoothly joined by pieces of quadratic potential curves.

The quantum tunneling in the symmetric double well is spontaneous and active,while in asymmetric double well,even the strength of the electric field is little the quantum tunneling disappears completely.

Phase transition and entanglement entropy of Bose-Einsteincondensates in double-well trap under periodic modulation;

Influence of noise on self-trapping of Bose-Einstein condensates in double-well trap;

Self-trapping and its periodic modulation of Bose-Einstein condensates in double-well trap;

Using numberical method,the paper studies resonanc transmission of a symmetric double well-potential in one-dimension,and the relations of resonance transmission with the width of potential well,of the space between of two potential well and of the energy of incident particular.