One-particle Schrödinger operators

Teschl, Gerald

R.A. Frick

We consider a particular four-dimensional generalization of the transition from the Heisenberg to the Schrödinger picture. The space–time independent expansion with respect to the unitary irreducible representations of the Lorentz group is applied, as Fourier transformation in the Heisenberg picture, to the states of a massive relativistic particle. A new Hamilton operator has been found for such a particle with spin one.

Zahriddin Ishkobilovich Muminov, Актамова Васила Уктамовна

We consider the Hamiltonian of a system of three quantum particles (two identical bosons and a fermion) on the one-dimensional lattice interacting by means of zero-range attractive or repulsive potentials. We investigate the point spectrum of the three-particle discrete Schrödinger operator H(K), K ∈ T which possesses infinitely many eigenvalues depending on repulsive or attractive interactions, under the assumption that the bosons in the system have infinite mass

Melih Kızılkaya

Helge Holden, Arne Jensen

Josef Janyška, Marco Modugno

We analyse the Schrödinger operator for a quantum scalar particle in a curved spacetime which is fibred over absolute time and is equipped with given spacelike metric, gravitational field and electromagnetic field. We approach the Schrödinger operator in three independent ways: in terms of covariant differentials induced by the quantum connection, via a quantum Lagrangian and directly by the only requirement of general covariance. In particular, in the flat case, our Schrödinger operator coincides with the standard one.