Some difficulties and developments in quantum mechanics

Durrani, Ijaz

Volodymyr Krasnoholovets

The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave ψ-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, etc. The probabilistic formalism is developed in the phase space, but not in the real one. Elimination of the difficulties is likely if we are able to develop quantum mechanics in the real space. Such a theory in fact can be constructed, however, it should proceed from deepest first principles starting from the notion of a 4D space-time, the notion of a massive particle in the space, the principles of the motion of a particle, etc. The theory should be characterized by short-range action that automatically means the introduction of a quantum mechanical force. It is shown that the aforementioned force makes it evident and, moreover, is able to appear on the macroscopic scale. A simple experiment, the express test, which in fact proves the macroscopic manifestation of quantum mechanical force, is proposed for the demonstration in the quantum curriculum.

Guangtian Zhu, Chandralekha Singh, N. Sanjay Rebello +2 more

We describe some common difficulties advanced undergraduate and graduate students have with concepts related to quantum measurement. We administered written tests to students enrolled in quantum mechanics courses and interviewed a subset of them to probe the difficulties in-depth and analyze their possible origins. Results from this research can be applied to develop learning tools to improve students' understanding of quantum measurement.

Y. Nambu

D. Baye, M. Dufour, Benjamin Fuks E

David Finkelstein, J. M. Jauch, Samuel Schiminovich +1 more

A new kind of quantum mechanics using inner products, matrix elements, and coefficients assuming values that are quaternionic (and thus noncommutative) instead of complex is developed. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The role played by the new imaginaries is studied. The principal conceptual difficulty concerns the theory of composite systems where the ordinary tensor product fails due to noncommutativity. It is shown that the natural resolution of this difficulty introduces new degrees of freedom similar to isospin and hypercharge. The problem of the Schrödinger equation, ``which i should appear?'' is studied and a generalization of Stone's theorem is used to resolve this problem.