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QM Ocillator

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data
    The wave function [tex]\Psi[/tex](x,t) ofr the lowest energy state of simple harmonic oscillator, consisting of a particle mass m acted on by a linear restoring force F=Cx, where C is the force constant, can be expressed as..
    [tex]\Psi[/tex](x,t)=Aexp[-([tex]\sqrt{}Cm[/tex]/2h)x[tex]^{}2[/tex]-(i/2)([tex]\sqrt{}C/m[/tex])t] where A is constant.

    a. use the Hamiltonian operator with V(x)=.5x[tex]^{}2[/tex], to evaluate the total energy of the state!


    2. Relevant equations
    Hop(x)=(P[tex]^{}2[/tex]op/2m)+V(x)
    Hop(t)=i*hbar(d/dt)
    P[tex]^{}2[/tex]op=-hbar[tex]^{}2[/tex]d[tex]^{}2[/tex]/dx[tex]^{}2[/tex]

    3. The attempt at a solution
    ok i am very confused as to which operqator to use, since my wave function is not time independent, but they give me V(x) value...
    but to find to total energy all u do is multiply the operator by wave function i think.

    can i ask which op do i use?? and is it just multiplying them together?
     
  2. jcsd
  3. Apr 9, 2009 #2
    they should give the same answer as its the same state!

    but seeing as it says in the question to use the Hamiltonian with [itex]V(x)=\frac{1}{2}x^2[/itex], i'd use the first one you wrote down seeing as it has a V(x) term in it.
     
  4. Apr 9, 2009 #3
    ok thanks
     
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