Quantum
Mechanics
Quantum
Mechanics
| Concepts | High School Syallbus | Quantum Mechanics History |
| Non- Locality | Photoelectric effect | Max Planck on Black Body radiation |
| Uncertainty Principle | Light Quanta | Einstein support Planck's suggestion |
| Wave particle duality | Line Spectrum | Schrodinger and Heisenberg |
| Einstein debates | ||
| Further developments. |
Imagine 2 space capsules that are linked by a narrow tube containing an electron. The electron has an equal probability of going into either of the capsule. Each capsule has a cat. If the electron goes to one capsule, a mechanism will trigger to kill the cat. The 2 capsules are then flown to opposite sides of the universe. When we do not look into the capsules, we do not know the states of the cat and the electron. But when we look into one, the state is determined and the probabilities in the other capsule is immediately determined to be a particular state.
Hence it seems that, by observing one capsule, the other capsule immediately takes on a particular state because the other capsule "knows that" the first capsule is observed.
Uncertainty Principle
The Uncertainly Principle states that measurement
affects the properties of the particles. The other form of definition is
that no two measurements can take place simultaneously, when one is measured
precisely, the other is blurred.
Defining "equalities"
Using the first equation as example, measuring the position (x) of the electron using violet waves (Which have smaller wavelength), the position can be known accurately. As violet waves are energetic, the momentum (p) gets chaotic. The converse case is true for using red waves to measure position.
Wave properties of light are widely known, as they are the only possiblities to explain interference, or the two slit experiment.
Particle properties of light are exhibited in the photoelectric effect and are impossible to explain the two slit experiment.
Particle properties of matter are taken for granted, such as the keyboard and computer.
Wave properties of matter are deduced by Louis de Broglie and are confirmed when electrons show interference when passing through crystal lattice. An application of electron waves is in the use of the electron microscope.
This is simply the shining of "light" (electromagnetic
waves) on a piece of metal and electrons are found to be ejected from the
metal surface.
Here's the setup.
Photoelectric setup.
Experiment results:
1. Number of electrons depend on intensity of "light"
2. Kinetic energy of electrons depend on wavelength or frequency of
"light" used.
3. No time lag from shining "light" to ejection of electrons.
Classical Wave Theory Predicts
1. There is a time lag for the electrons to eject because energy from
wave comes continously.
2. Kinetic energy depends only on intensity of "light".
Quantum Theory Explains
1. There is no time lag as the energy arrives in packets which are
fully absorbed by the electron.
2. The greater the intensity, the more electrons are ejected, as there
are more energy packets.
3. By the equation, E = hf, (h is a constant), energy depends on the
frequency used.
Einstein Sets the Foundation.
The energy packet is called a photon. By the conservation of energy:
hf = hfo + kinetic
energy of the electrons
hf is the energy of the photon
hfo is the minimum energy required to eject an electron,
also known as "work function energy".
Hence light is also thought to exist as particles or photons.
Newton is the first to imagine light as particles but he is opposed by Christian Huygens. Only when Thomas Young performed the double slit experiment then the particle theory is abandoned.
James Clerk Maxwell at the end of the 19th century showed that light is an electromagnetic wave and the particle theory is completely ignored. It was only revived by Max Planck in the start of the 20th century.
Energy of photon = hf
h is the Planck's constant 6.63 x 10-34 Js
f is the frequency of the light
Since speed of light, c = frequency x wavelength
Energy of photon = hc / wavelength
This is the discovery that actually electrons in the atom occupy quantised energy levels around the nucleus.
How do you explain this:
Absorption Spectra
Emission Spectra
Explaination with quantised energy levels:
Consider an electron with such energy levels:
When photons corresponding to the difference between the 2 energy levels
are absorbed for the transition, an absorption spectra is seen.
When electrons descend to the lowest energy state, photons are emitted,
with energies corresponding to the difference between the 2 levels. Hence
an emission spectra is seen.
Actual situation.
Emission Spectra
Absorption Spectra
Black Body Radiation Curves.
Black body is a body that absorbs all the radiation falling on it and is also a perfect emitter of radiation. Black body radiation is the thermal radiation that would be emitted from a black body at a particular temperature.
In the 19th century, physicists were puzzled why a heated piece of metal can turn from red to yellow, then to white hot. By using wave properties of light to calculate, they found that at high frequencies, the energy radiated is infinity. This problem is known as the "Ultraviolet Catastrophe".
Max Planck approached the problem in 1900 in another way: he assumed that the energy are in discrete packets. He avoided the "catastrophe" and got a set of results that fitted the experimental values well. The physics community did not accept this idea as Maxwell's wave equations of light are accurate to predict properties of light.
Einstein support Planck's suggestion
In 1905, Einstein, using Planck's idea of a quanta, to explain the photoelectric effect . Using Planck's constant of 6.63 x 10-34 Js to calculate the kinetic energy of the photoelectrons, he obtained values that are close to experimental data. Once again, the wave theory of light is at stake.
In 1923, a young French prince and physics graduate student, Louis de Broglie, wrote the basic relations that a "matter-wave" should obey, stating that an electron should have a definite frequency and wavelength, just like light waves.
de Broglie's work
In 1926, Erwin Schrodinger formulated the Schrodinger Wave Equation to predict the properties that these matter waves should obey. At the same time, Heisenberg uses Matrices to formulate the same theory to predict the properties of matter-waves.
The most important work of Heisenberg is that, the Universe is no longer deterministic with his Uncertainty Principle.
Einstein although won the Nobel's Prize for the photoelectric effect, was against the theory of quantum mechanics.
He was against that the theory of probablities can be used to formulate the theory that explained the microworld.
He argued that the theory is incomplete as a complete
theory must deal individual entities but quantum mechanics deal with group
behaviour.
He was against the "reality" that the Universe is
non-objective.
Further developments.
In the later years, the wish is to unify the theory
of Quantum mechanics and Relativity, or find a theory that shows that the
four fundamental forces; strong, weak nuclear forces, electromagnetic force
and gravity, are different forms of a fundamental force.
The first step is that the electromagetic force and the weak nuclear force is unified. In 1967-68, Steven Weinberg, Abdus Salam, and Sheldon Glashow, noticed that these two forces have the same energy at a particular state, thus they are actually different forms of the same force with Z0, Z1 and W particles as force carriers.
The next step is to unify the electro-weak theory with Quantum Chromodynamics (QCD). QCD is the theory that proposes the quark model and the strong nuclear force is actually transmitted by gluons between quarks. The proton and the neutron are made up of triplets of quarks. This unification is achieved with the proposal of Grand Unified Theory (GUT) in 1974. The problem with this GUT is that it is very difficult to verify. Trillions of electrovolts are needed.
The final step is to put gravity into the main picture and get the Ultimate truth of how the universe works. The possible way is to extend symmetry to gravity with the theory of Supersymmetry. Another way is to extend the dimensions in the Universe to ten with the theory of Superstrings.
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