History of Quantum mechanics

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History of Quantum mechanics
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Max Planck

• He explained the energy spectre in black body
  radiation by supposing that energy exchange
  between the walls of a black body and the
  radiation was discontinuous. The exchange between
  the walls and radiation happened with packets of
  energy hf. Here h is Plancks constant and f
  the frequency of the radiation

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Black body radiation

• Planck found a formula for black body radiation
  by supposing that the atoms in the walls could be
  described at harmonic oscillators and that these
  oscillators had energy given by the formula nhf
  where n was a whole number, h Plancks constant
  and f the frequency of the radiation.
• The minimum energy to be sent out was then.
• E nhf- (n-1)hf hf
• Since there was a minimum energy to be sent out
  the energy was quantised.

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Albert Einstein

• He in 1905 submitted three works as he worked
  on the patent office in Bern Switzerland. It vas
  
• The special theory of relativity.
• The explanation of the photoelectric effect
• A theory for Brownian motion.

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Albert Einstein

• In the theory for photoelectric effect
  Einstein says that electromagnetic radiation with
  a certain frequency f in reality consists of a
  stream of energy particles photons. Where the
  energy of a single photon is given by h f. In
  1921 Einstein gets the Nobel price in physics for
  this work
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Photelectric effect

• Light falls on a metal surface
• Then we can observe that electrons is emitted
• Whether electrons are emitted or not depends on
  the frequency of the light

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Photoelectric effect

• Incoming energy photon Kinetic energy electron
  work to get loose from metal
• hf 1/2mev2 W

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Ernest Rutherford

• He explored the atom by sending ?-particles
  against a foil of gold. Most particles went
  trough where as a few were thrown back. This led
  Rutherford to conclude the atom had to have a
  positive nucleus where most of the mass was
  concentrated. Round this mass the negative
  electrons circulated.

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Problems with Rutherfords theory of the atom

• When the electron circulates round the nucleus
  it has an acceleration. According to the theory
  of electromagnetic radiation it then should send
  out radiation. Sending out energy this way it
  should lose energy and spiral down to the
  nucleus.
• Another problem was to explain the line
  spectra of radiation emitted by gases

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Niels Bohr

• To solve this problems Niels Bohr set forth
  the following postulates.

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Bohrs postulates

• The atom can only exist in special stationary
  states with energy E1.En, without sending out
  energy.
• If an atom goes from state Em to a state with
  less energy En, the difference in energy will be
  sent as a photon.
• hf Em En
• The angular moment of the electron is quantized.
• mvr nh/2

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Bohrs result

• From the last postulate Bohr could deduce that
  the energy levels of the Hydrogen atom was given
  by the formula
• En -B/n2
• This formula explained the Hydrogen spectre,
  but it could not explain the spectre of other
  gases where the atoms have more than one
  electron.

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Werner Heisenberg

• Heisenberg tried to move on from Bohrs
  orbits which were unobservable and concentrate on
  what was observable. That was the energy and the
  frequency of the radiation. He set up these
  observations in tables witch he manipulated and
  so he developed the matrix version of Quantum
  mechanics.
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Uncertainty principle

• A consequence of Heisenbergs version of
  Quantum mechanics is the there is a downward
  limit for how detailed one can observe a certain
  pairs of observables at the same time. One such
  pair is position x and momentum p for a particle.
  Another pair is energy of a system E and the time
  t one has to observe that system.
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Uncertainty principle

• Vi have
• ?x?p ? h/4?
• ?E?t ? h/4?
• Where h is Plancks constant

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De Broglie

• He meant that as waves had connection with
  particles maybe particles was connected to waves.
  

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Wave and particle

• The momentum is p mv
• For a photon the effective mass is
• m E/c2 m hf/c2
• And the speed is that of light c. Then
• p (hf/c2)c p hf/c p h/?
• De Broglie supposed this was general such that
  we could turn the equation and for any particle
  with momentum p, get an associated wave where the
  wavelength was given by
• ? h/p

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Ervin Schrødinger

• Inspired by De Broglie he developed a general
  Quantum mechanics based on wave equations.
  Schrödinger and Dirac later showed that his wave
  version of Quantum mechanics was equivalent to
  Heisenbergs matrix version

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Max Born

• In general the wave function lies in the
  complex plane. The square of the wave function
  however, gives a real number. Max Born proposed
  that this number was the probability for a
  certain observation

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Paul Dirac

• Dirac developed a relativistic version of
  Quantum mechanics. One of the consequences of
  this was that all particles should have
  antiparticles. Another consequence was that
  particles should have the property of spin

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Wolfgang Pauli

• He formulated Paulis exclusion principle
  which later was developed into the general
  difference between fermions and bosons. He also
  predicted the existence of the neutrino, which
  was found in 1956.

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John von Neumann

• He was a mathematician and developed in 1932
  what was considered the final version of Quantum
  mechanics.
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EPR-paradox

• To show that Quantum mechanics was incomplete
  Einstein, Podolsky and Rosen proposed the
  following. A stasjonary particle disintegrates
  into two particles. By measuring the momentum of
  one of the particles we know the momentum of the
  other since momentum is conserved. We then can
  find the position of this particle. Since we
  already know the momentum we dont have to worry
  that a precise measurement of position will give
  a less precise value for momentum. Thereby we can
  get behind Heisenberg uncertainty principle
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John Stewart Bell

• In 1964 he came with a theory which showed
  that it experimentally was possible to test
  between Bohrs and Einsteins view of Quantum
  mechanics. In 1982 Alan Aspect made observations
  which most physicists think supports Bohrs view
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