**Quantum Mechanics**

The primary difference between the
**Newtonian Mechanics Model**
of the universe and the
**Quantum Mechanics Model**
is that **Newtonian Mechanics** treats particles as points and **Quantum Mechanics** treats them as three dimensional "waves."

These are "waves" in a sea of probability.
A particle is like a water molecule in the volume of the wave, i.e., its location is not fixed within the wave.
As the wave moves, the molecule can be located at different places in the wave.
In the **Quantum Model**, if the molecule is exactly located in the wave, neither the speed nor direction of the molecule's motion can be determined.
This is the essence of the
**Uncertainty Principle**
of the universe and the
One can locate a particle at an exact point in space but a wave is "spread out" allowing only a "most probable" location
to be determined.
This is contrary to what our five senses perceive but, as technology extends these senses, we observe phenomena that are only accurately
described by the **Quantum Mechanics Model**.
**Quantum Mechanics** is wierd and counter-intuitive but it works.

Because scientists must now deal with "waves," not "points," statistics is a necessary mathematical tool.
The statistical **probability** that a particle will be located at a specific point in space replaces the exact three **Newtonian**
spacial coordinates (x,y,z) for the particle.
A **Quantum Mechanical** location statement for a particle is called a **Wave Function**.

The principle of **Superposition** requires that the mathematics of **Quantum Mechanics** reduce to those of **Newtonian Mechanics**
under "normal" conditions.
For example, when **Quantum Mechanics** is used to describe the motion of a ball on a pool table, the extra terms and factors
in the **Quantum Mechanical** equations are trivial and, when these trivial terms and factors are ignored, the equations of motion
look exactly like those of **Newtonian Mechanics**.

The **Quantum Mechanics** model is constructed using sets of **Quantum Numbers** and statistical **Operators**.
The **System** under examination determines the **Quantum Numbers** which are specified.
A **System** might be a single particle, a valence electron of an atom, an atomic nucleus, or a neutron star.
These **Quantum Numbers** are "plugged into" the **Operators** resulting in a second set of **Quantum Numbers**.
The "new" set of **Quantum Numbers** describe the **System** under "new" conditions, usually at a different time, past or future.