making sense of quantum mechanics a wikiversity collaborative project aiming to present quantum...
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Making sense of Quantum Mechanics
A wikiversity collaborative project aiming to present
Quantum Mechanics in an intuitive perspectivehttp://en.wikiversity.org/wiki/Making_sense_of_quantum_mechanics
Arjen Dijksmanmail:materion at free.fr
web: http://materion.free.frblog: 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)
Addition rule for vectors (a set of vectors is just another vector)
All we do is draw little arrows, that’s
all.
Richard Feynman
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Orientation of the vector evolves (1/2)
Vectors of the generalized evolution law
1
2
3
4
5
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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
Arrow spinning in its pilot wave
Tout se passe comme si l'Ether
et la Terre avaient le même
mouvement de translation...
Maurice Allais
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Interaction between two particles
E1
E2 =2E1vE1
t
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Collision between two particlest
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Other spinning modes
z
y
x
z s
a) s=2z
b) s=-2z
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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