6. Quantum mechanics as a linear theory

Alexander G. Kyriakos

The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.

Arnold Neumaier, Dennis Westra

P. Nattermann

We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of nonlinear quantum theories.

LW Yu, Wang NL, Shigeru Kanemitsu

Anticipating the realization of quantum computers, we propose the most reader-friendly exposition of quantum information and qubits theory. Although the latter lies within framework of linear algebra, it has some flavor of quantum mechanics and it would be easier to get used to special symbols and terminologies. Quantum mechanics is described in the language of functional analysis: the state space (the totality of all states) of a quantum system is a Hilbert space over the complex numbers and all mechanical quantities are taken as Hermite operators. Hence some basics of functional analysis is necessary. We make a smooth transition from linear algebra to functional analysis by comparing the elements in these theories: Hilbert space vs. finite dimensional vector space, Hermite operator vs. linear map given by a Hermite matrix. Then from Newtonian mechanics to quantum mechanics and then to the theory of qubits. We elucidate qubits theory a bit by accommodating it into linear algebra framework under these precursors.