Nonrelativistic quantum particles on the Minkowski plane

Abstract

The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schrödinger equations for eigenvalues are obtained using the Beltrami-Laplas operator of the pseudo-Euclidean plane and the corresponding potentials. It is shown that, in contrast to the standard problem on Euclidean plane, in addition to the continuous spectrum, a free particle has a discrete energy levels and a Coulomb particle, in addition to the discrete spectrum, has unstable states that describe the incidence of a particle on isotropic lines forming a metric cone.

References in corpus (6)

• Relativistic Harmonic Oscillator Revisited
• Dyon-Oscillator Duality
• Wavefunction for the Universe Circa the Beginning with Dynamically Determined Unique Initial Conditions
• Extended Rindler Spacetime and a New Multiverse Structure
• Some Aspects of Quantum Mechanics of Particle Motion in Static Centrally Symmetric Gravitational Fields
• Quantum mechanics of stationary states of particles in external singular spherically and axially symmetric gravitational and electromagnetic fields