Making sense of Quantum Mechanics A wikiversity collaborative project aiming to present Quantum Mechanics in an intuitive perspective Arjen Dijksman mail:materion at free.fr web: blog: 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

Wikiversity Project: Making sense of Quantum Mechanics2 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

Wikiversity Project: Making sense of Quantum Mechanics3 Quantum system is represented by a vector quantum system of needlesIts 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

Wikiversity Project: Making sense of Quantum Mechanics4 Orientation of the vector evolves (1/2) Vectors of the generalized evolution law

Wikiversity Project: Making sense of Quantum Mechanics5 Orientation of the vector evolves (2/2) The generalized Schrödinger equation (evolution law)

Wikiversity Project: Making sense of Quantum Mechanics6 Example: Particle in a box Arrow bouncing back and forth between both walls (animated gif)

Wikiversity Project: Making sense of Quantum Mechanics7 Example: Particle in a box Arrow bouncing back and forth between both walls (animated gif)

Wikiversity Project: Making sense of Quantum Mechanics8 Example: Particle in a box Arrow bouncing back and forth between both walls (superposition)

Wikiversity Project: Making sense of Quantum Mechanics9 Example: Particle in its wave Arrow spinning in its pilot wave

Wikiversity Project: Making sense of Quantum Mechanics10 Example: Particle in its wave Arrow spinning in its pilot wave

Wikiversity Project: Making sense of Quantum Mechanics11 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

Wikiversity Project: Making sense of Quantum Mechanics12 Interaction between two particles E1E1 E 2 =2E 1 v E1E1 t

Wikiversity Project: Making sense of Quantum Mechanics13 Collision between two particles t

Wikiversity Project: Making sense of Quantum Mechanics14 Other spinning modes

Wikiversity Project: Making sense of Quantum Mechanics15 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

Wikiversity Project: Making sense of Quantum Mechanics16 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