On the Feasibility and Usefulness of Applying the Schrödinger Equation to Quantum Measurement

Willem M. de Muynck

The present paper is a sequel to papers dealing with recent developments on the issue of `quantum measurement'. In this paper `measurement within the domain of application of quantum mechanics' is treated as a \emph{quantum mechanical} \emph{interaction} of a `(sub)microscopic object $(o)$' and an `equally (sub)microscopic part of the measuring instrument $(a)$ being sensitive to the (sub)microscopic information', that interaction to be described by a Schrödinger equation. The Stern-Gerlach experiment is used as a paradigmatic example. An alternative to the Heisenberg inequality is found, exhibiting the \emph{independent} contributions of `preparation of the initial state of object $(o)$' \emph{and} `interaction of object $(o)$ \emph{and} measuring instrument/probe $(a)$'. Applicability of the Liouville-von Neumann equation is stressed.

Bi Qiao, Harry E. Ruda

H. W. L. Naus

C. Pacheco‐García, Jesús García‐Ravelo, J. Morales +1 more

Abstract Exactly solvable Schrödinger equation (SE) with a position‐dependent mass distribution allowing Morse‐like eigenvalues is presented. For this, the position‐dependent mass Schrödinger equation is transformed into a standard SE, with constant mass, by means of the point canonical transformation scheme. In that method, the choice of potential for the position‐dependent mass Schrödinger equation allows us to obtain the transformation that should be used to find the exactly solvable SE. As a useful application of the proposal, the equivalent of the Witten superpotential is chosen to be constant to find the position‐dependent mass distribution and the exactly solvable potential V(m(x)) allowing Morse‐type energy spectra. This V(m(x)) is shown to have a Coulomb potential structure and can be useful in the study of the electronic properties of materials in which the carrier effective mass depends on the position. Moreover, the worked example, the approach is general and can be applied in the search of new potentials suitable on the study of quantum chemical systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Jeffrey Bub

Paul Kinsler

I present an alternative and rather direct way to derive the well known Schrödinger equation for a quantum wavefunction, by starting with the Klein Gordon equation and applying a directional factorization scheme. And since if you have a directionally factorizing hammer, everything looks like a factorizable nail, I also derive an alternative wavefunction propagation equation in the momentum-dominated limit. This new Schrödinger $p$-equation therefore provides a potentially useful complement to the traditional Schrödinger $m$-equation's mass-dominated limit.