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Help!-energy eigenstates

  1. Nov 1, 2004 #1
    if we have a potential of the form V(x) = a|x|, how would one go about estimating the ground state energy of the system using the heisenberg uncertainty principle.

    I suppose the thing to do is to get an estimate of delta x, then get delta p via the heisenberg uncertainty principle and the E = delta p^2/2m but the particle could be anywhere on the real axis since the potential is finite on the interval (-inf,inf)!
    any hint much appreciated
  2. jcsd
  3. Nov 2, 2004 #2
    I don't understand how you would estimate the ground state energy using Heisenberg uncertainity principle. However what I would do to estimate the groundstate energy is to use the variational principle. To use the variational principle you need to guess a form of the ground state wave function. So for this case the ground state wave function would be symmetric. So try a Gaussian form psi(x) = exp(-x^2/a^2), with a being the variational parameter. You can refer to "Modern Quantum Mechanics", JJ Sakurai, pg 313.
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