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How does one develop a Hamiltonian for a free particle?

  1. Jul 8, 2007 #1
    The equation for the Hamiltonian is H = T + V. Can someone explain how you can use this to get this equation for a free particle:

    [tex]i\hbar|\psi'> = H|\psi> = P^2/(2m)|\psi>[/tex]

    The first part is obviously Schrodinger's equation but how do you get H = P^2/2m?

    Go to page 151 at the site below if you do not understand this question.

    http://books.google.com/books?id=2z...sig=nQ9UgEufWOeqXgJdtGEylDqK7ok#PRA1-PA151,M1
     
    Last edited: Jul 8, 2007
  2. jcsd
  3. Jul 8, 2007 #2
    For a free particle V=0.

    You're left with the KE operator.

    Classically, KE=p^2 /2m.

    QM, KE operator = p^2 / 2m, with p=-ihbar d/dx (in 1D)
     
  4. Jul 9, 2007 #3
    I see. Thanks.
     
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