help!-energy eigenstates

[ee7klt]

hi,
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

[gouthambs]

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.
Goutham