Making sense of Quantum Mechanics

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Making sense of Quantum Mechanics

• A wikiversity collaborative project aiming to
  present
• Quantum Mechanics in an intuitive perspective
• http//en.wikiversity.org/wiki/Making_sense_of_qua
  ntum_mechanics
• Arjen Dijksman
• mailmaterion at free.fr
• web http//materion.free.fr
• blog http//commonsensequantum.blogspot.com

Problem 2 Resolve the problems in the
foundations of QM, either by making sense of the
theory as it stands or by inventing a new theory
that does make sense. Lee Smolin
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Summary

• What are the first principles of Quantum
  Mechanics?
• A quantum system may be represented by a vector
• The orientation of the vector representing a
  quantum system evolves
• Kets are transformed into other kets by means of
  operations that reveal an observational property
• In quantum measurements, the result is always
  undetermined
• Quantum probabilities involve interaction cross
  sections of both observed and observing particles
• Examples
• Particle in a box, particle in its wave,
  collision of particles
• Do Quantum mechanics and Classical Mechanics
  address the same questions?
• Path for a classical particle is that of least
  action
• Most probable path for a quantum particle is that
  of least action

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Quantum system is represented by a vector
quantum system of needles
Its representation as vectors (or kets)
All we do is draw little arrows, thats
all. Richard Feynman
Addition rule for vectors (a set of vectors is
just another vector)
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Orientation of the vector evolves (1/2)
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Vectors of the generalized evolution law
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Orientation of the vector evolves (2/2)
The generalized Schrödinger equation (evolution
law)
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Example Particle in a box
Arrow bouncing back and forth between both walls
(animated gif)
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Example Particle in a box
Arrow bouncing back and forth between both walls
(animated gif)
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Example Particle in a box
Arrow bouncing back and forth between both walls
(superposition)
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Example Particle in its wave
Arrow spinning in its pilot wave
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Example Particle in its wave
Arrow spinning in its pilot wave
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Example Particle in its wave
Tout se passe comme si l'Ether et la Terre
avaient le même mouvement de translation... Mauri
ce Allais
Arrow spinning in its pilot wave
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Collision between two particles
t
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Classical Mechanics vs Quantum Mechanics (1/2)
In classical mechanics, an elementary particle is
represented by a point that follows a path of
least action
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Classical Mechanics vs Quantum Mechanics (2/2)
In QM, an elementary particle is represented by a
vector whose most probable path is that of least
action