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numexercises7_14 [2014/07/14 08:43] bogner |
numexercises7_14 [2014/07/14 10:29] bogner |
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* Check numerically that the constructed HO wf's are orthonormal. To do this, you will want to use Gaussian quadrature to discretize the integrals. Gaussian quadrature is discussed a bit in {{:ho_spherical.pdf| }}. If you don't have a routine to calculate quadrature points/weights, take advantage of Google to find a canned routine to do this for you. | * Check numerically that the constructed HO wf's are orthonormal. To do this, you will want to use Gaussian quadrature to discretize the integrals. Gaussian quadrature is discussed a bit in {{:ho_spherical.pdf| }}. If you don't have a routine to calculate quadrature points/weights, take advantage of Google to find a canned routine to do this for you. | ||
- | * Construct a subroutine that returns relative HO matrix elements of the Minnesota NN potential. The definition of the Minnesota potential is here: | + | * Construct the hamilton matrix $\langle nl|H|n'l\rangle$ keeping all HO basis states $n,n'<N_{max}$. Diagonalize the matrix for increasing $N_{max}$ values for different values of the oscillator length parameter $b$ ("oscl" in the code.) $b$ and $\hbar\omega$ are related by $b = \sqrt{(\hbar/(m\omega)}$. Plot your lowest eigenvalue for each $N_{max}$ as a function of $b$ (or $\hbar\omega$). |
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+ | * Construct a subroutine that returns relative HO matrix elements of the Minnesota NN potential. The definition of the Minnesota potential and a sketch of how to proceed will be given on the black board. | ||
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+ | Here are | ||