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12_variation_perturbation_matrixhq

# 0 2 a diagonal h is a solved problem solving a problem

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Unformatted text preview: n Basis Functions are Not Eigenfunctions of the Hamiltonian x 0 a Use particle-in-a-box basis set, , to solve a new problem where there is a potential of within the box basis set functions are not eigenfunctions or ramp Hamiltonian and evaluate matrix elements ∗ , ∗ ∗ 2 2 , 2 ∗ 2 let Mathcad evaluate these integrals numerically Now H is not diagonal, it must be “diagonalized” to solve the problem. Run the Mathcad program “matrix_particleinabox_voltage.xmcd” Particlein-a-Box Mathcad Program “matrix_particleinabox_voltage.xmcd” at first set to zero, which is just the particle-in-a-box problem 0 nmax 6 pick the max number of basis functions set up indices over the basis functions i 0 nmax 1 a 10 set constants for problem, atomic units m 1 a j 0 nmax 1 hbar 1 0.0 Hamiltonian Matrix Elements - Note that the eigenvector and eigenfunction routines need the origin of matrices to be zero. Our first wavefunction has a quntum number of one, not zero. As a result, this expression adds one to the "i" and "j" indices to shift from the inex to t...
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