Relativistic Schrodinger equation. II

Frank V. Kowalski

Fatemeh Ahmadi, Afshin Shafiee

As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is assumed to be composed of a probability field joined to a particle called a particle-field or PF system. The relativistic generalization of this theory and its invariance under Lorentz transformation has been proved. In this essay, based on the relativistic generalization of Schrodinger equation derived in [4], we solve the relativistic Schrodinger equation for relativistic micro-harmonic oscillator to find its energy. Also we obtain the energy spectrum of Hydrogen atom that is the main purpose of this paper. We see that the result is completely consistent with the relativistic correction to the Hydrogen's energy in first-order perturbation theory.

Hosung Sun

Based on the exact quantization rule for the nonrelativistic Schrodinger equation, the exact quantization rule for the relativistic one-dimensional Klein-Gordon equation is suggested. Using the new quantization rule, the exact relativistic energies for exactly solvable potentials, e.g. harmonic oscillator, Morse, and Rosen-Morse II type potentials, are obtained. Consequently the new quantization rule is found to be exact for one-dimensional spinless relativistic quantum systems. Though the physical meanings of the new quantization rule have not been fully understood yet, the present formal derivation scheme may shed light on understanding relativistic quantum systems more deeply.

Sergio Cecotti

Helmut Scheffers

Nickola Stefanov Todorov