# 8.6: Variational Method in MAPLE


The variational method is exceptionally well suited to computer algebra packages such as maple. The procedure is as follows:

• Define Trial wavefunction $$\Phi$$
• Evaluate Normalization factor $$|c^2 | = \langle \Phi |\Phi \rangle$$
• Evaluate unnormalised kinetic energy $$\langle T \rangle = −\hbar^2 \langle \Phi |\nabla^2 |\Phi \rangle /2m$$
• Evaluate unnormalised potential energy $$\langle V \rangle = \langle \Phi |\hat{V} |\Phi \rangle$$
• Differentiate with respect to variational parameters $$D_{a_n} = \frac{d}{da_n} (\langle T \rangle + \langle V \rangle )/c^2$$
• Solve $$D_{a_n} = 0$$ for all $$a_n$$
• Substitute optimal value for $$a_n$$ into $$\Phi$$.
• Evaluate $$[\langle T \rangle + \langle V \rangle ]/c^2$$ using optimised wavefunction.

If one needs to do another variational calculation for a different potential and trial wavefunction, only definitions 1 and 3 need to be changed.

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