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Observables of position and momentum have a continuous spectrum

  1. Dec 3, 2005 #1
    could someone explain this paragraph taken from "concepts of modern physics" by arthur beiser pg175? i'm having trouble understanding it...

    "A dynamical variable G may not be quantized. In this case, measurements of G made on a number of identical systems will not yield a unique result but instead a spread of values whose average is the expectation value
    <G>=(integrate) G(psi^2)dx"

    and why if the electron's position in the hydrogen atom isn't quantized, we have to think of the electron in the vicinity of the nuvleus with a ceratian probability?
     
  2. jcsd
  3. Dec 3, 2005 #2

    Galileo

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    Some physical observables can take on discrete (quantized) values, like the energy of a particle in an infinite potential well, harmonic oscillator, or the energy of the electron in an hydrogen atom. In this case the eigenvalue-spectrum of the corresponding observable is discrete. This is not always the case though. The observables of position and momentum have a continuous spectrum (ie, not quantized).
    The expectation value is calculated the same way as with any observable:
    [tex]<G>=<\psi|G|\psi>[/tex]

    So the position of the electron in a hydrogen atom in not quantized (it's after all described by a continuous wavefunction) and thus given by a probability density |psi|^2
     
  4. Dec 3, 2005 #3
    thank you very much for explaining!!!:)
     
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