Problems of the Fourdimensional Scalar Product in Quantum Mechanics

G. P. Pronko

Edward L. Hill

Won Sang Chung, HASSAN HASSANABADI

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

Stefano De Leo, Gisele Cristina Ducati

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.

Laurent Baulieu, J. Iliopoulos, Roland Sénéor

Abstract Time-ordered products and connection with the path integral. Applications in quantum mechanical problems. T-products and the scattering matrix. The perturbation expansion. The scalar field.