Aspects of Degeneracy

Yukio‐Pegio Gunji

A model for a system consisting of elements which detect the measurement apparatus of other elements is proposed. By any apparatus one can observe locally, however it can refer to non‐local property because apparatus itself is indefinite. In taking this aspect into consideration, I formulate expressions for a local interaction referring to non‐local property. This formalization can satisfy the aspect of what is called, internal measurement. This system shows teleological global motion toward criticality which is relevant to the degeneracy of a specific element featuring D ? Hom(Z), E) by which infinite time and space are renormalized.

Laro Schatzer, Wolfgang Breymann, H. Thomas

Harry A. Mavromatis

Pranawa C. Deshmukh, Aarthi Ganesan, N. Shanthi +3 more

The Schrödinger equation does not account for the 2n2 degeneracy of the hydrogen atom, which it dismisses as an “accidental” degeneracy. The factor of “2” in the 2n2 degeneracy is well-accounted-for in the relativistic formulation by the two spin states of the electron. The n2 degeneracy is nevertheless not quite an “accident”; it is due to the SO(4), rather than SO(3), symmetry of the hydrogen atom. This result is well known, but is inadequately commented upon in most courses in quantum mechanics and atomic physics, leaving the student wondering about the origins of the n2 degeneracy of the hydrogen atom. A pedagogical analysis of this interesting aspect, which highlights the fundamental principles of quantum mechanics, is presented in this article. While doing so, not only is the n2 degeneracy of the hydrogen atom explained, but its energy spectrum and eigenfunctions are obtained without even using the Schrödinger equation, employing only the fundamental principles of quantum mechanics rather than the Schrödinger equation.

Harry A. Mavromatis