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Expectation Value

  1. Jun 28, 2008 #1
    We all know the concept of expectation value,it is the average of all possible outcomes of an experiment. Mathematically average of x is written as (Σnkxk / Σnk ). Quantum-mechanically nk is represented by probability density(P), where P = ∫Ψ*Ψ d3r,
    then <r> = ∫ r P(r) d3r -----------(1)
    or <r> = ∫ Ψ*(r) r Ψ(r) d3r--------(2) (normalisation condition)
    but when we consider expectation value of Energy operator (= ih∂/∂t) the two equations ,to me, not give the same results. Can anybody solve what’s that dilemma and where I am wrong
     
  2. jcsd
  3. Jun 28, 2008 #2
    The expectation of an operator H is defined as <[itex]\Psi[/itex]|H|[itex]\Psi[/itex]>. The form (1) above holds only under special circumstances.

    Note: H = ih∂/∂t is the energy operator only when expressed in the position representation.

    Pete
     
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