Monday, May 5, 2014

quantum mechanics - Why do we need infinite-dimensional Hilbert spaces in physics?


I am looking for a simple way to understand why do we need infinite-dimensional Hilbert spaces in physics, and when exactly do they become neccessary: in classical, quantum, or relativistic quantum physics (i.e. when particles can be created and destroyed)?


I would like to understand both physical interpretation and the mathematical point of view - what exactly becomes ill defined in the mathematical formalism - is it the commuation relation for quantum mechanics or something else?




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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...