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Quantum Rigid Rotator

  1. Apr 28, 2007 #1
    Hi! I have been doing some problems to prepare for my physics final and came across this series which I have not been able to solve and was hoping someone here might be able to help me out with.

    The problem is that of a two-dimensional rigid rotator which rotates in the xy plane and has angular momentum Lz=-ih ∂/∂t

    It is in cylindrical coordinates.


    - hbar^2/(2I) d^2Φ(φ)/(dφ^2) = EΦ(φ)


    dT(t)/(dt) = -iE(T(t))/hbar

    Here E is the separation constant; also, Φ(φ)T(t)=Ψ(φ,t)

    First of all we must solve the equation for the time dependence of the wave function just listed.

    Second show that the separation constant is the total energy.

    One solution is Φ(φ)=e^imφ where m = sqrt[2IE]/hbar

    Third apply the condition of single-valuedness.

    The allowed values of energy are E=hbar^2m^2/(2I) when abs[m] = 0,1,2.....

    Fourth normalize the funcions Φ(φ)=e^imφ found previously.

    I SINCERERLY appreciate any help!!!
  2. jcsd
  3. Apr 29, 2007 #2
    if Lz=(h/i)*(∂/∂φ), how can u write the energy in terms of the operator Lz?

  4. Apr 29, 2007 #3
    All you have to do to find the energy in terms of L is:

    E=.5Iω^2 +0potential = .5I(L/I)^2 = L^2/(2mr^2)

    because L=Iω and I=mr^2.

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