Prognostication on the P-list

[Dave Monroe]

At the beginning of the twentieth century,
experimental evidence suggested that atomic particles
were also wave-like in nature. For example, electrons
were found to give diffraction patterns when passed
through a double slit in a similar way to light waves.
Therefore, it was reasonable to assume that a wave
equation could explain the behaviour of atomic
particles.

Schrodinger was the first person to write down such a
wave equation. Much discussion then centred on what
the equation meant. The eigenvalues of the wave
equation were shown to be equal to the energy levels
of the quantum mechanical system, and the best test of
the equation was when it was used to solve for the
energy levels of the Hydrogen atom, and the energy
levels were found to be in accord with Rydberg's Law.

It was initially much less obvious what the
wavefunction of the equation was. After much debate,
the wavefunction is now accepted to be a probability
distribution. The Schrodinger equation is used to find
the allowed energy levels of quantum mechanical
systems (such as atoms, or transistors). The
associated wavefunction gives the probability of
finding the particle at a certain position.

http://www.physlink.com/Education/AskExperts/ae329.cfm

In physics, the Schrödinger equation, proposed by the
Austrian physicist Erwin Schrödinger in 1925,
describes the space- and time-dependence of quantum
mechanical systems. It is of central importance to the
theory of quantum mechanics, playing a role analogous
to Newton's second law in classical mechanics.

In the mathematical formulation of quantum mechanics,
each system is associated with a complex Hilbert space
such that each instantaneous state of the system is
described by a unit vector in that space. This state
vector encodes the probabilities for the outcomes of
all possible measurements applied to the system. As
the state of a system generally changes over time, the
state vector is a function of time. The Schrödinger
equation provides a quantitative description of the
rate of change of the state vector....

http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

The Schrodinger Wave Equation

http://online.redwoods.cc.ca.us/DEPTS/science/chem/storage/Schrod/index.htm

Visual Schrödinger: A Visualizer-Solver Applet for the
One-Dimensional Schrödinger Equation

http://fermi.la.asu.edu/Schroedinger/html/Schroedinger.html

--- Otto <ottosell at googlemail.com> wrote:

> The last sentence:
> 
> "This eq. replaces the Schrödinger equation."
> 
> ... whatever that means!

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