Measurability of the Schrödinger Wave

Yakir Aharonov, Lev Vaidman A

Yakir Aharonov, Lev Vaidman

James McNeill, James E. Bidlack

This paper discusses the relativistic Schrödinger differential wave equation for the hydrogen atom and hydrogen-like cations, which have measured ionization energies from hydrogen to the Cu 28+ hydrogen-like cation.The analytical solution to the relativistic Schrödinger differential wave equation correlates with experimental data if the angular momentum quantum number l >0.For quantum levels with l = 0 , the analytical solutions predict ionization energy values larger than that measured for the hydrogen atom and hydrogen-like cations.Also, beyond the element erbium, Z > 68 for l=0 quantum states, the analytical solution yields energy values that are complex numbers.This is similar for the Dirac relativistic differential wave equation which fails for nuclei that have an atomic number larger than 137.Using measured 1s ionization energy values of hydrogen-like cations, a numerical solution to the relativistic Schrödinger differential wave equation is possible since an analytical one is not when the measured ionization energy is different from the analytical result.In addition, since the analytical solutions to the radial part of the relativistic Schrödinger differential wave equation are complicated, normalized numerical solutions are less difficult to obtain using Microsoft Excel.Most differential equations do not have analytical solutions, and, therefore, only numerical solutions are possible utilizing boundary or initial conditions. Classical Schrödinger Differential Wave Equation and Wave-Particle Duality in Quantum Mechanics

José Maria Filardo Bassalo, P. T. S. Alencar, D. G. da Silva +2 more

In this paper we study the quantum wave packet of the Schrodinger equation for continuous quantum measurements.

Chen, Zeqian

It is shown that `bipartite' wave functions can present a mathematical formalism of quantum theory for a single particle, in which the associated Schrödinger's wave functions correspond to those `bipartite' wave functions of product forms. This extension of Schrödinger's form establishes a mathematical expression of wave-particle duality and that von Neumann's entropy is a quantitative measure of complementarity between wave-like and particle-like behaviors. In particular, this formalism suggests that collapses of Schrödinger's wave functions can be regarded as the simultaneous transition of the particle from many levels to one. Our results shed considerable light on the basis of quantum mechanics, including quantum measurement.

Donald D. Fitts