TITLE:
A Simple Remark Leading to a Basic Precision Estimate for Non-Relativistic (NR) Real Values of Quantum Mechanics Operators
AUTHORS:
Amaury de Kertanguy
KEYWORDS:
Atomic Physics, Planck Constant, Schrödinger Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.4,
April
25,
2018
ABSTRACT: Starting
with a very basic statement that any physical constants cannot be written with
an infinite precision, it is shown how to introduce this uncertainty into the Hamiltonian
of non-relativistic atomic (NR) physics and how to estimate errors on quantum
operators (energy, frequency, momenta) when an uncertainty is assigned
to . The Schrödinger equation is written and the
kinetic energy term is
transformed into a Laplacian: . This transformation leads (as known since 1926) to
the wave equation, whose solutions are wave functions. The relativity
correction to the kinetic energy term is introduced and its effect is
discussed. (h constant has an uncertainty value taken
from CODATA.)