Exact solution of the Schrödinger equation for a particle in a regular N-simplex

E. N. Maslen, Paul C Abbott, J E Gottschalk +1 more

H. Almström

K. Schmitt, P.‐G. Reinhard, C. Toepffer

We investigate the validity of the time-dependent Hartree-Fock (TDHF) approximation for a finite fermion model system. With the help of coherent states we derive equations of motion for the one-particle density, which are of classical Hamiltonian form and can be interpreted in terms of generalized coordinates and momenta. The corresponding trajectories in phase space show transitions between regular and chaotic regimes depending on the parameters of the model. A chaotic behavior indicates a failure of the TDHF approximation because the exact solutions are always regular due to the linearity of the Schr\"odinger equation.

C. Tezcan, R. Sever

Irene M. Moroz, Roger Penrose, Paul Tod

As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrödinger-Newton equations. For a single particle, this is a coupled system consisting of the Schrödinger equation for the particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the n th solution having n zeros in the wavefunction. Furthermore, these are the only globally defined solutions. Analytical support is provided for some of the features found numerically.

E. E. Perepelkin, Б. И. Садовников, Наталья Германовна Иноземцева +1 more