Wave Function

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Wave Function

• jiyanjiang_at_gmail.com
• 2007-09-26

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Some history

• 1925-1926, Heisenberg, Born, Jordan, matrix
  mechanics
• same time, Schrodinger, wave mechanics
• 1930, Dirac
• Nonrelativistic quantum mechanics
• Relativstic quantum mechanics
• Feynman path integral
• Quantum field theory(QFT)

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No body understands it
I think it is safe to say that no one understands
Quantum Mechanics. (Richard Feynman) The more
you see how strangely Nature behaves, the harder
it is to make a model that explains how even the
simplest phenomena actually work. So theoretical
physics has given up on that. (Richard Feynman,
Quantum Mechanics) What I am going to tell you
about is what we teach our physics students in
the third or fourth year of graduate school... It
is my task to convince you not to turn away
because you don't understand it. You see my
physics students don't understand it. ... That
is because I don't understand it. Nobody
does. (Feynman, Richard P. Nobel Lecture, 1966,
1918-1988, QED, The Strange Theory of Light and
Matter)
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Wave function

• From de Broglies idea, a state is represented by
  a wave function, not by (r, p).
• Thus, we get a quantum mechanical description of
  a system.

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What is wave function

• It is not a real physical quantity.
• But we can get all possible physical information
  from it (wave function). By this meaning, wave
  function is a complete description of a system.

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Borns statistical interpretation
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But in some cases

• For example, we measure a particles position (x)
  and momentum (p), we can never get simultaneous
  measurements of x and p, exactly. (recall
  uncertainty relations)
• But in classical mechanics, we can get x, and p
  simultaneously.
• Is quantum mechanics a complete theory or not.
• Einstein think QM is a incomplete theory.
• Others (Bohr, Heisenberg, ) think QM is a
  complete theory.

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Hidden variables?

• the position of the particle was never
  indeterminate, but was merely unknown to
  experiment.
• Thus wave function is not a complete description,
  some additional information--called hidden
  variable, exists but unknown--is needed to
  provide a complete description of the particle.

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Orthodox opinion

• Measurement theory, plane wavethe particle
  wasnt anywhere, but a combination of all
  placesact of measurementforced the particle
  jump to a certain position randomlythe
  probability proportional to \psi 2.
• Copenhagen interpretation Observations not only
  disturb what is to be measured, they produce it,
  We compel the particle to assume a definite
  position. Jordan (quoted by Mermin, is the
  moon there when nobody looks?)

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Bells inequality

• Up to now, Bells inequality is violated, hence
  the orthodox opinion is defensed.

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Readings

• Bransden Joachain, Atomic and Molecular
  Physics, Section 2.1, 2.2
• David J. Griffiths, Introduction to Quantum
  Mechanics, Section 1

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Problems

• ?????????,??1,??2
• David J. Griffiths, Introduction to Quantum
  Mechanics Problem 1.13, 1.15, 1.18 (??)