A few model Λ-nucleus potentials are proposed which explain the ground state binding energy data of⁵He and thep-shell hypernuclei satisfactorily. Potential-II is capable of distinguishing the hypernuclei of the same mass number but of differentN andZ values. The dependence of this potential on (N − Z) term indicates that there is a charge symmetry breaking component in ΛN force. Alongwith the earlier density dependent effective Λ-nucleus interaction, these potentials may be used to determine approximately the density distributions of light nuclei. From these potentials an estimate ofD_Λ is also made. It is found to be in conformity with the earlier estimates.

The binding energy of the double hypernucleus_ΛΛ⁶ is calculated in α + 2Λ cluster model using the method of translation invariant basis TIMO. As regards the required interaction potentials we use a density dependent effective ΛN force and a gaussian form for ΛΛ potential. With these interactions a very reasonable value ofB_ΛΛ is obtained if the oscillator states up to the excitation quantum numberN=12 are taken into account in the expansion of wavefunction of the hypernucleus. This value ofN is much smaller than that obtained in an earlier study. This lowering inN value is attributed to a much better choice of ΛN potential used in the present study.

We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (𝑛_𝑥, 𝑛_𝑦, 𝑛_𝑧) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various closed orbits. The closed orbits are possible for certain specific values of quantum numbers (𝑛_𝑥, 𝑛_𝑦, 𝑛_𝑧) and initial momenta (𝑘_𝑥, 𝑘_𝑦, 𝑘_𝑧). We observe that a cubical billiard exhibits degenerate energy levels and the path lengths of the closed orbits for these degenerate energy levels are identical. In spite of the identical path lengths, the shapes of the closed orbits for degenerate levels are different and depend upon angles 𝜃 and 𝜙 which we term as the sweep and the elevation angles, respectively. These degenerate levels owe their origin to the symmetries prevailing in the cubical billiard and these levels disappear completely or partially for a parallelepiped billiard as the symmetry breaks due to commensurate or incommensurate ratio of sides.