XPost: sci.physics, sci.math, sci.physics.particle   
   From: david250@videotron.ca   
      
   On 05/30/2012 04:53 PM, Shmuel (Seymour J.) Metz wrote:   
   > In, on 05/29/2012   
   >     at 10:22 PM, David Bernier  said:   
   >   
   >> psi(X) evolves with time.  A measurement is represented   
   >> by an unbounded hermitian operator A .  If psi is the   
   >> wave-function, psi will jump to new-psi, where   
   >> A.new-psi = lambda * new-psi, lambda a real number.   
   >   
   > That would be true[1] if the Hilbert space were finite dimensional,   
   > but QM uses an infinite dimensional Hilbert space, and some operators   
   > have continuous spectra.   
      
   Oops. In the case of measurement of the x-coordinate,   
   for an electron-wave psi,   
      
   is there a relation (of the measurement operator)   
     to  "x times psi", where psi is a function of space   
   coordinates x, y and z?   
      
      
      
   >> Quantum systems, when measured,   
   >> are found to be in states "Up", "Down"   
   >   
   > Up and down are eigenspaces of a spin obsevable, not states.   
      
      
   Ok.  Up and down are eigenspaces for the measurement of spin   
   operator along some axis.   
      
   ==   
      
   John von Neumann wrote a tome:   
      
   "Mathematical Foundations of Quantum Mechanics",   
      
   < http://books.google.ca/books?id=JLyCo3RO4qUC > .   
      
   ===   
      
   I'm not sure I understand the difference between a "pure state"   
   and a "mixed state" ...   
      
   David   
      
      
      
      
   > [1] Assuming that you believe in the Copenhagen interpretation.   
   >   
      
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