Framework of Quantum Mechanics

Erhard Scheibe

Aishwarya Parthasarathi

The study of the non-Hermitian Hamiltonian systems within the framework of Supersymmetric Quantum mechanics (SUSY QM) has been carried out in literature in the last decade. Most of these potentials are either PT Symmetric or quasi-Hermitian in nature. But no formulation is advanced in literature to the study of general complex potentials within its framework. In this paper, using the complex phase space approach, we carry out the complexification of Supersymmetric Quantum Mechanics to enable the study of any general non-Hermitian Hamiltonian system within its framework. The commutation relations among its operators are enumerated and the underlying symmetry is discussed. The eigenvalues and eigenfunctions of the real and imaginary parts of superpartner Hamiltonians are also investigated.

A. J. Sakaji, Ignazio Licata, A. J. Sakaji +6 more

Framework for QFD in 3-D Space .............................................................188 12.5 Quantum Fluid Dynamical Equations within a Density Functional Framework..................................................................................................191 12.6 Miscellaneous Aspects of the Quantum Fluid Dynamical Approach .........193 12.7 Concluding Remarks...................................................................................194 Acknowledgments..................................................................................................194 Bibliography ..........................................................................................................194 The concepts of quantum mechanics (QM) are so radically different from those of classical mechanics that soon after Schrödinger proposed the concept of quantum mechanical wavefunction, there were attempts to provide a classical interpretation of QM. In fact, the success of Madelung [1] in transforming the Schrödinger equation into a pair of hydrodynamical equations consisting of the continuity equation and an Euler type equation of hydrodynamics, giving birth to so-called quantum fluid dynamics (QFD) [2-5], in 1926, itself is testimony to the strong urge to have a classical interpretation of the strange world of QM. The concept was resurrected with full vigor more than 25 years later through the pioneering works of Bohm [6] and Takabayashi [7]. In the meantime, Wigner [8] introduced, in 1932, the concept

O. Tapia

The photonic framework offers clues leading to a possible update of the foundations of quantum mechanics yet preserving its mathematical grounds. Reconsideration of quantum theoretic measurement theory warrants removal of ideological prejudices brought in by von Neumann Copenhagen interpretation. Conditions required to bridge abstract to laboratory space formulations of QM permit underscoring fundamental differences to the standard view; entanglement and sustainment concepts help in this task. Entanglement events integrate probing devices leading to q-measurements seen as physical processes. Representation elements based on classical physics pictures are removed. A non-representational framework stands up as a result.

Iulia Georgescu