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We have studied wavepacket dynamics in the Razavy hyperbolic double-well (DW)potential which is coupled to a harmonic oscillator (HO) by linear andquadratic interactions. Taking into account the lowest two states of DW and$(N+1)$ states of HO ($N=1$ to 10), we evaluate eigenvalues and eigenfunctionsof the composite system. An analytical calculation is made for $N=1$ andnumerical calculations are performed for $1 < N \leq 10$. Quantum tunneling ofwavepackets is realized between two bottoms of composite potential $U(x,y)$where $x$ and $y$ denote coordinates in DW and HO potentials, respectively. Ithas been shown that with increasing $N$ and/or the coupling strength, thetunneling period is considerably increased. Phase space plots of $\langle x\rangle$ vs. $\langle p_x \rangle$ and $\langle y \rangle$ vs. $\langle p_y\rangle$ are elliptic, where $\langle \cdot \rangle$ denotes an expectationvalue for the two-term wavepacket. This result is quite different from therelevant one previously obtained for the quartic DW potential with the use ofthe quantum phase space representation [Babyuk, arXiv:0208070]. Similarity anddifference between results calculated for linear and quadratic couplings, andthe uncertainty relation in the model are discussed.

Wavepacket dynamics in a quantum double-well system with Razavy's potential coupled to a harmonic oscillator