Quantum theory
Many students that are going into physics major as a master degree might not have
the basis of Quantum theory. I recommend students pursuing physics as major to consider
reading my paper to get a heads up of what they will be progressively learning from entering
physics courses through to their master’s degrees. Quantum theory is a very large and wide
science but my focus is going to be about the evolution of quantum theory (history), the
uncertainty principle of this theory and the probability wave functions of quantum theory. The
uncertainty principle describes what the particles in the subatomic level acts. What I just
mentioned is not quit appropriate because from the name we get the glance that it’s uncertain
so how can we describe an uncertain quality. There are two experiments that are done by
scientists to understand the behavior of particles in such environment. The two experiments
are the double slit experiment and the Schrödinger cat paradox. I will introduce how those
experiments were performed and a full analysis of its connection to the uncertainty principle.
Probability wave functions are what scientists use to determine the position of an electron in a
system. I will demonstrate a simple understanding of how physics uses these probability
functions to determine positions, trajectories and behaviors of an electron. Yes I said positions,
trajectories and behaviors because after reading and understanding quantum theory; one
electron might have multiple positions, trajectories and behaviors at the same instant of time.
Quantum theory is the study of matter and energy in the subatomic level. Scientist through
their experiments and observance found out that electrons or matter at the subatomic level act
in a very unpredictable way!
In 1900 physicist Max Planck presented his quantum theory to the German Physical
Society. Plank study was concerned around the radiation of heated materials. He developed a
new formula that describes that the radiation are emitted or absorbed in discrete unit of
energy called quanta. Plank continued his researched and came up with a new universal
constant called plank’s constant ( h is 6.63 * 10E-34 Js). His formula E=f*h stated that the
multiplication of the radiation frequency by planks constant is equal to quantum. This was
revolutionary in the field of theoretical physics because it contradicts our way of thinking about
energy and radiations in classical physics. That was the first assumption of quantum theory.
In 1905 Albert Einstein used Planck's relationship to explain the results of the
photoelectric effect which showed that the energy E of ejected electrons was dependent upon
the frequency f of incident light as described in the equation E=hf. It is ironic that in 1921 Albert
Einstein was awarded the Nobel Prize for this discovery, though he never believed in particles
and acknowledged that he did not know the cause of the discrete energy transfers (photons)
which were contradictory to his continuous field theory of matter!
In 1913 Bohr published his model of atomic structure introducing the theory of
electrons traveling in orbits around the atom's nucleus. Bohr also introduced the idea that an
electron could drop from a higher-energy orbit to a lower one, emitting a photon (light
quantum) of discrete energy. This became a basis for quantum theory.
In 1933 Erwin Schrödinger received the Nobel Prize for his contribution to quantum
mechanics. Erwin Schrödinger proposed an experiment in 1935 known by Schrödinger's cat.
Schrödinger's cat is a famous illustration of the principle in quantum theory of superposition,
Schrödinger's cat serves to demonstrate the apparent conflict between what quantum theory
tells us is true and what we observe to be true about the nature and behavior of matter in
classical physics.
How do we see different colors? The reason why an object has a color is the fact that
certain atoms absorb for instance green frequency of light and then re-radiate green light back
to our eyes. This confirms what plank’s postulated about absorbing and emitting in a discrete
unit of energy but now it applies to atoms or particles as well. We conclude that atoms absorb
and emit energy or frequencies in a certain discrete values
Figure 11.1: Discrete Energy Levels of Hydrogen
We always visualized an atom as our solar system where the sun is the nucleolus and
the planets are the electrons rotating around it in a precise trajectory. But this believe can’t
physically work, electromagnetic theory states that an accelerating charged body radiates until
it loses all its charge. If an electron loses its charge it will eventually hit the nucleolus which
implies that the solar system model collapses with such explanation. Classical physics fails to
describe the subatomic level and contradicts all what we know about chemistry and the
reactions that have been proven to work experimentally. H2o to such science isn’t water it is an
unstable substance that can’t exist. This really limited classical physics to macro systems and
made physicist look or come up with a new science that describes the subatomic world. Bohr
postulated that the atom is made of positive particles, making up the nucleolus, and negative
particles called electrons that move around the nucleolus. The electron can only exist in certain
special allowed states where the electron can accelerate without radiating (losing energy).
Electrons can jump from state to a higher state when they absorb energy equal to the energy
difference between the two states or go to a lower state by radiating the energy difference
between the two different states. Bohr also said that the electron in the lowest state which he
called the ground state will no longer radiate. This postulation had a big impact on old quantum
theory especially because mathematically it was able to compute the radius of the hydrogen
atom.
The standard explanation of what takes place at the quantum level is known as the Copenhagen
Interpretation. This is because much of the pioneering work was carried out by the Danish
physicist Niels Bohr, who worked in Copenhagen. This is a very complex theory, and in order to
fully do it justice it would require at least a fair sized book. However, in order to grasp the basic
principles involved it will be sufficient enough to study just two key experiments. The two
experiments are generally known as Schrödinger's Cat in the Box Experiment and the Double
Slit Experiment.
Schrödinger's 'Cat-in-the-Box Experiment:
It is a very simple experiment to do but a very hard experiment to interpret and
understand. We imagine an apparatus containing just one Nitrogen-13 atom and a detector
that will respond when the atom decays. Connected to the detector is a relay connected to a
hammer, and when the atom decays the relay releases the hammer which then falls on a glass
containing poison gas. We take the entire apparatus and put it in a box. We also place a cat in
the box, close the lid, and wait 10 minutes. Then we ask is the cat dead or alive? Quantum
mechanics’ answer for this question is 50% alive and 50% dead. According to Schrödinger, the
cat remains both alive and dead (to the universe outside the box) until the box is opened. When
we open the box the probability function collapses and then one of the two states is present,
either dead or alive. In other words the act of observation will cause it to become one or the
other. If you are confused by this you are not alone. I do not think anyone has a good
understanding of what is going on here although many physicists are firmly convinced of the
correctness of the interpretation they favor. My own inclination is to think that Einstein was
correct, and we need a deeper theory to explain events, like the decay of a particle, that will
dispatch Schrödinger's poor cat.
Double Slit Experiment:
This experiment was first observed in the study of optics where a beam of light was shot
to a two separate tiny slits and the result was observed on a screen. The result was an
interference pattern which shows that light has a wave like properties versus our previous
knowledge that Einstein introduced about light having a particle like properties called photons.
Light is not our concern but it has similar properties with that of an electron.
Figure 11.14: Interference Experiment with Bullets
Figure 11.14 shows how the experiment is done. As we can see there are two slits and a
source shooting bullets in all directions. The result will produce two probability waves P1(X)
and P2(x).
P12(x)=P1(x)+P2(X), where P12(x) represent the over all probability distributions
of real bullets. There is no interference in the sense that a bullet will reach a point x on the wall
by either taking a path through slit 1 or through slit 2.
Figure 11.15: Interference Experiment with water waves
A similar experiment is performed for water wave as shown in Figure 11.15. The
detector can only measure the intensity of the wave, which is proportional to the square of the
height of the wave. If we only consider slit one to be open and slit two to be closed we will end
up with a probability wave
1(x) that represents the intensity of the wave passing through
slit one. If we consider the opposite where slit one is closed and slit two is open we end up with
a probability wave 2(x) that represents the intensity of the wave passing through slit two.
When slits one and two are open, the resultant intensity is given by
The reason why the intensity of the interference pattern is not the sum of the individual
amplitude is due to the constructive and destructive interference of waves. In other words the
merging of the two waves coming out from slit one and slit two will result in an interference
pattern as shown in fiqure11.15.
To ascertain whether an elementary particle such as an electron behaves like a wave or
particle, we carry out the interference experiment similar to the one we have considered for
water waves. What we need to state at the outset that the interference patterns P12(x) and
12(X) can both be obtained for the electron depending on how we perform the experiment. The
experimental arrangement consists of an electron gun which sends identical electrons through
a screen which has two slits to a wall where an apparatus keeps track of the point at which the
electron stops. The electron gun produces the electrons one by one, so that at any given time
there is only one electron traveling from the electron gun to the wall. We consider two
different experiments with this arrangement. One experiment in which a measurement is
carried out to determine which slit the electron went through and a second experiment in
which no measurement is made to determine which slit the electron goes through. In both
cases a large number electrons are sent in, one by one, and the distribution of the positions at
the electron is at is measured.
Experiment with Detection
Figure 11.16: Electron with detectors
We perform the experiment as given in Figure 11.16 with both slits 1 and 2, open and with the
additional requirement that we determine which slit the electron actually passes through. This
can be arranged by fixing two detectors at the back of the slits as shown in Figure 11.16. Since
we know which slit the electron goes through we can plot three distribution curves. P1(x) and
P2(x) are the distribution curves for electrons go through slit 1 and slit 2 respectively. Similar to
the result obtained for bullets, the probability of the electron arriving at a point on the wall when
both slits are open is the sum of P1(x) and P2(X)
P12(x) is the distribution curve for electrons that passes through either slit 1 or 2. We
consequently have the result that when the electron's path is measured, it has a particle-like
behavior.
Experiment without Detection
Figure 11.17: Electron without detectors
Consider now the same experiment as before, but with the detectors removed, In other
words, we do not make any measurement to determine which slit the electron goes through.
The result of this experiment shows that a single electron gives rise to interference. The
interference pattern P12(x) is exactly like
12(X) as obtained for water waves. The superposition
principle is the unique feature of quantum mechanics, and shows graphically that, under some
circumstances, particles behave as probability waves.
Reference page
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Quantum theory, Retrieved October 4, 2009, from
http://www.thebigview.com/spacetime/quantumtheory.html
What is quantum theory, Retrieved October 4, 2009, from
http://searchcio-midmarket.techtarget.com/sDefinition/0,,sid183_gci332247,00.html
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Quantum Mechanic history, Retrieved October 4, 2009, from
http://www.gap-system.org/~history/HistTopics/The_Quantum_age_begins.html
A Brief history of quantum mechanics, Retrieved October 3, 2009, from
http://4physics.com/phy_demo/QM_Article/article.html
Definition from whatis.com, Schrödinger’s cat experiment, Retrieved October
5,2009,from
http://whatis.techtarget.com/definition/0,,sid9_gci341236,00.html
Quantum mechanics introduction: Physics, Retrieved October, 5, 2009, from
http://whatis.techtarget.com/definition/0,,sid9_gci341236,00.html
http://www.laundry-alternative.com/fateofmissingsocks.htm
Picture References
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hubpages.com/.../physics/quantum-mechanics/3826
http://srikant.org/core/node12.html