The basic logic of quantum mechanics

Quantum Mechanics (Winter, 2012)

January 16, 2012

Professor Susskind introduces the simplest possible quantum mechanical system: a single particle with spin.  He presents the fundamental logic of quantum mechanics in terms of preparing and measuring the direction of the spin.  This fundamental logic differs from classical systems in that it is entirely about probabilities, and therefore is very different from classical boolean logic.

Professor Susskind then reviews the concept of vector spaces and describes the vector space for a single spin system.  He concludes the lecture by relating the concept of orthogonality in vector spaces to overlaps in configuration or phase space.  More precisely orthogonal vector space states correspond to a lack of overlap in configuration space.

  • Single spin system
  • Basic logic of quantum mechanics
  • Vector spaces
  • Basis vectors
  • Analogy between vector space and configuration space