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Double well potential is V ( x ) = λ ( x 2 - a 2 ) 2
We set the parameters: = 1 ; m = 1 ; a = 2 ;
The Mathematica notebook, given a potential V(x), allows to numerically solve the equation, finding the energies (eigenvalues) and the relative functions (eigenfunctions).

λ = 0.5

λ = 1.0

λ = 1.5