Cosmology, Astronomy and Modern Physics

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Quantum Mechanics
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The New Quantum Era
Erwin Schrödinger 1887-1961
Werner Heisenberg 1901-1976
Paul Dirac 1902-1984
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Wave-particle duality

• Applying this to the atom
• Heisenberg saw a way to resolve the particle and
  wave concept of an electron without using the
  Bohr model

Max Born 1882-1970
Born suggested matrix mechanics
Worked.but no physical picture
Paul Ehrenfest and Pascual Jordan 1880-1933
1902-1980
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Schrödinger

• Matter waves? - Schrödinger wave equation
• Wave function ? describes amplitude of wave
• wave mechanics

1-dimensional Schrödinger equation
Erwin Schrödinger 1887-1961
Quantum mechanics aims to find ? in a certain
situation (e.g. for an electron in an atom)
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What does it mean?

• Whole subject in itself
• We will look at how ? can be interpreted
• Amplitude of matter wave?

Max Born 1882-1970
?2 can be interpreted to represent the
probability of finding the electron at a given
position at a certain time
No certainties...
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Double-slit - revisited

• One electron at a time seemingly random picture

Am. J. Phys. 57 117 (1989)
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Double slit -probabilities

• High peaks represent high ?2 high probability

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Measurements

• We know that we cant measure very precisely -
  always errors
• If you measure the weight of a rock, how accurate
  can you be?
• If you measure the length of something?

Absolute limit to accuracy Not down to
instruments but to nature.
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Heisenberg

• The actual act of measuring leads to an
  uncertainty in the measurement

Werner Heisenberg 1901-1976
Overall, the combined uncertainty is given by
Heisenbergs uncertainty principle
You cant measure both the position and momentum
of an object precisely at the same time.
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Example

• Say that we can measure the position of an object
  so that the uncertainty is ?x 1.2 x 10-11m.
  Determine the minimum uncertainty in the momentum
  of the object.

4.4 x 10-24 kg ms-1
Very small uncertainty in momentum! What effect
would this have?
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Example continued

• If this was an electron (m9.1 x 10-31 kg), what
  would be the uncertainty in its speed? What if
  it were a baseball (m0.15kg)?

p mv so ?p m?v and thus ?v ?p/m
?v (electron) (4.4 x 10-24) / (9.1 x 10-31)
4.8 x 106 ms-1 ?v (baseball) (4.4 x 10-24) /
(0.15) 2.9 x 10-23 ms-1
So very small uncertainty in velocity of baseball
(negligible) but MASSIVE uncertainty in velocity
of electron. Think of it round the other way - if
you know the velocity...
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Uncertainty 2

• Distance is related to time (?t ?x/v)
• Energy related to the velocity (momentum) hf
  hv/?
• So another version of the uncertainty principle
  is

This would, in principle, allow us to borrow
large amounts of energy for a very short period
of time
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Quantum Measurement

• The very act of measurement affects what youre
  measuring
• States indeterminate until they are measured
• collapse of the wavefunction

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Schrödingers Cat

• Schrödinger unhappy with the probabilities...
• ? Famous thought experiment.

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The cat is dead and alive?

• Until we open the box and observe, we dont know
  if the decay has happened or not
• The cat is dead
• The cat is alive

superposition of states
But once we make the observation open the box
we collapse the wavefunction. Maybe the cat does
this by itself
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Copenhagen Interpretation

• In honour of Niels Bohr

• A collection of ideas
• Ideas of probability, complementarity and
  self-consistency

Bohr at Los Alamos
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Dirac

• Synthesis of relativity and quantum theory
• Prediction of anti-matter

Paul Dirac 1902-1984
1932 investigation of cosmic rays
Found particle with mass of electron, but
positive charge positron
Carl Anderson 1905-1991
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Cloud Chamber

• Gas cooled to condensation point
• High energy particles leave droplets behind

Charles Wilson 1869-1959
See also bubble chamber
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Solvay, 1927
Heisenberg
Schrodinger
Pauli
Debye
Bragg
Dirac
Compton
Born
de Broglie
Bohr
Planck
Curie
Lorentz
Einstein
Wilson
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EPR paradox

• Einstein, Podolsky and Rosen
• Separation of two entangled particles

Measuring the properties of one automatically
defines the properties of the other Spooky
action at a distance Non-locality
John Bell 1928-1990
Alain Aspect b. 1947
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Many Worlds Interpretation

• collapsing wave function unsatisfactory
• Hugh Everett, 1957 (PhD thesis)

Hugh Everett III 1930-1982
Cat is dead and alive Different realities
Strange, but it works gt 50 acceptance amongst
physicists (?)
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The Macroscopic World

• Cartoon

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Back to reality

• We saw earlier that X-rays were of a suitable
  wavelength to be diffracted by crystals (of the
  order of 10-10 m)

Clifford Schull 1915-2001
Neutrons (m1.675 x 10-27 kg) so
Put ?10-10m v 4000 ms-1
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Nuclear Physics

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