### Re: What is the Quantum Nature of Atoms, in general?

Date: Wed Apr 25 14:14:21 2007
Posted By: Joe Fitzsimons, Grad student, Quantum and Nanotechnology Theory Group, Department of Materials, Oxford University
Area of science: Physics
ID: 1173714997.Ph
Message:
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Hi Aaron,

it would be impossible for me to give you any kind of definitive answer.
Instead, I will try to give you a general overview of what quantum
mechanics is and how it can be applied to atoms, followed by some

In quantum mechanics we describe the state of a system either in terms of a
wave function, or in terms of a state vector. These descriptions are to
different, but equivalent, ways of looking at the problem. In either case,
we need what is called a basis of orthogonal states. What this basically
means is that we need a set of states with the property that when we
measure the system we are gauranteed that it will be in one of those
states. One example of a basis for a single particle is position. If we try
to measure the position of a particle we will only ever see it in one
place, and will never measure it to be in 0,2,3... places at the same time.

Where quantum mechanics differs from our everyday experience is that it is
possible for a particle to have a wave function that is in what is called a
superposition of basis states. So what does this mean? Well basically it
means that a particle can be in a superposition of two or more positions at
the same time. When we try to measure the particle we will only get one
result, but we cannot know ahead of time which result. If a particle could
only be in one of, say, 3 possible states, then we could write its state
as: a|1> + b|2> + c|3>. Here I have used |1>, |2> and |3> to label the 3
possible basis states (this is known as Dirac notation, although there is
no need to worry about it at the moment). a,b and c are known as amplitudes
and are in general complex numbers (although you can think of them as real
numbers between -1 and 1 for this example). The probability of measuring
the particle to be in any state is given the square of the absolute value
of the amplitude. If we keep a,b and c as real numbers, as above, then the
corresponding probabilities are just a^2 (this means a squared), b^2 and
c^2. Since we must measure the particle to be in one of the states, we must
have a^2 + b^2 + c^2 = 1. This property of superposition is what separates
quantum mechanics from classical mechanics, which we experience every day.
At first most people don't believe that this incredible effect actually
happens, but it has been verified many times (see for example
http://en.wikipedia.org/wiki/Youngs_double-slit_experiment#Quantum_version_of_experiment).

Atoms are made up of a very small positively charged nucleus containing
protons and neutrons, around which are trapped electrons. The electrons are
bound to the neucleus because they are negatively charged, and opposite
charges attract. All of these particles are in a specific superpostion of
states known as a shell. The nucleus is very tightly bound, so the neutrons
and protons are spread over a very small area, while the much lighter
electrons are spread over a much larger area. When energy is added to an
atom (either through a collision with other particles, or when it absorbs a
particle of light known as a photon), the electrons are rearraged into a
different shell. The atom can only absorb light if it gives an electron
just the right amount of energy to move from one shell to another. Because
there is a gap between energy levels not all light can be absorbed. What
determines the energy of light is it's frequency, which we percieve as it's
colour. Different atoms and molecules have different arrangements of
shells, and so absorb and reflect different coloured light. This is what
gives materials their colour.

If an electron is in an excited state, it can drop down into a lower shell
emitting a photon. This is how light is 'made'. In a light bulb the
electricity (a flow of electrons through the filament) excites the atoms,
which then drop down into a lower energy level, while in the process
emitting light. By studying the light emitted, reflected or absorbed by
some material it is possible to determine what it is made of. This process
is known as spectroscopy.

For a general popular science introduction to quantum mechanics I would
suggest "In search of Schrodingers Cat" by John Gribbin, but if you are
interested in understanding the mathematics involved then I would suggest
volume 3 of the "Feynman Lectures" by Richard Feynman (he won the Nobel
Prize for physics in 1965 for his work on the interaction of particles with
light, inventing what is called quantum electrodynamics). This second book
is aimed at interested non-scientists, but introduces all the required
mathematics and physics in a very conversational manner. There is also four
videos online of Feynman giving introductory lectures at
http://www.vega.org.uk/video/subseries/8).

Joe

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