We single out seven essential features of quantum theory for atoms and molecules which carry over their significance to the quantum theory of human life.

These seven features are: 1) probability, 2) duality, 3) ways to influence atoms, 4) macroscopic variables, 5) independent variables, 6) symmetries, and 7) action principle

1. Probability: Let us give the simplest example of hydrogen atom. Hydrogen atom consists of one proton, which is positively charged, and one electron, which is negatively charged. The electron is circulating around the proton like a cloud.  We cannot find a definite position, 100% sure, of the electron in a given point in space. We can only say we can find, say 20% of time, that electron in a certain region of space around the proton.
   
2. Dual character of quantum theory. Wave and particle duality is one of the very first dual properties found out by founding fathers of quantum theory in early twentieth century. Light has both wave property and particle property. Light has definite wave length like a wave. Light is also a particle like tennis ball. When it hits the silicon chip in a solar cell, it knocks out one electron at a time.
   
3. There are three ways to influence the electrons in the electron beam of a television tube:
   
   
1. Boundary: The electron beam is in a vacuum tube. The glass of the vacuum tube provides the proper boundary for the space that the electron beam can move in.
2. Bound state: The electron beam is bound with the vacuum tube, which is bound in a television case. If the electron beam is not in the television case, there will be no television.
3. Exchange: In order to move the electron beam around inside the television, it is necessary to change the electric field that bends the electrons in the electron beam. Electric field in quantum field theory is the work of photons. Change of electric field is equivalent to exchange of photons between electrons with the electrodes.
   
4. There are macroscopic variables created for different systems of atoms and molecules. For example to describe the thermal properties of a piece of copper, we invent the macroscopic variables: temperature, pressure, conductivity, etc. These macroscopic variables do not have meaning for one copper atom, or even a few copper atoms.  But they are extremely valuable when we want to describe the properties of copper in our copper wires at home.
   
5. There are five fundamental variables for atoms: numbers, time, space, energy, and momentum: The important numbers for atoms are often referred to as quantum numbers. Quantum numbers come in integers or half integers.

Charges of an atom can only be 1, 2,  or -3. It cannot be fraction like 0.1241
To describe an electron inside the tube of a television set, we need to prescribe four independent variables: time, space, energy, and momentum.

6. Symmetry principles: One of the most sacred principles in physics, conservation of energy, can be derived from the translational symmetry in time. Gauge symmetry is the symmetry that guides us to reach the correct laws that govern quarks and electrons.
   
   
7. Action principle: The behavior of electron in hydrogen atom can be calculated to at least seven digit of accuracy that agrees precisely with experiment. The calculation comes from applying an equation of motion that can be derived from the action principle. Action principle is used to derive the equation of motion for all subatomic particles, including quarks and leptons.

It is our belief these seven qualitative features of quantum theory can give us deep and fundamental understanding of our daily life. Hence they will be very useful for us to learn and apply.

By SY Lo
2/9/2007