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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
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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