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1.3: Fundamental Principles of Quantum Mechanics

There is nothing special about the transmission and absorption of photons through a polarizing film. Exactly the same conclusions as those outlined above are obtained by studying other simple experiments, such as the interference of photons (see Dirac, Section I.3), and the Stern-Gerlach experiment (see Sakurai, Chapter 1; Feynman, Chapter 5). The study of these simple experiments leads us to formulate the following fundamental principles of quantum mechanics:

  1. Dirac's Razor. Quantum mechanics can only answer questions regarding the outcome of possible experiments. Any other questions lie beyond the realms of physics.
  2. Principle of the Superposition of States. Any microscopic system (i.e., an atom, molecule, or particle) in a given state can be regarded as being partly in each of two or more other states. In other words, any state can be regarded as a superposition of two or more other states. Such superpositions can be performed in an infinite number of different ways.
  3. Principle of Indeterminacy. An observation made on a microscopic system causes it to jump into one or more particular states (which are related to the type of observation). It is impossible to predict into which final state a particular system will jump. However, the probability of a given system jumping into a given final state can be predicted.

The first of these principles was formulated by quantum physicists (such as Dirac) in the 1920's to fend off awkward questions such as ``How can a system suddenly jump from one state into another?'', or ``How does a system decide which state to jump into?''. As we shall see, the second principle is the basis for the mathematical formulation of quantum mechanics. The final principle is still rather vague. We need to extend it so that we can predict which possible states a system can jump into after a particular type of observation, as well as the probability of the system making a particular jump.