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===== Numerical Exercises for Monday July 14 ===== | ===== Numerical Exercises for Monday July 14 ===== | ||
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+ | * Install Git, and try out some of the commands covered in Morten or Nicolas's lecture slides ({{:computing.pdf|}} {{:talentdftguides.pdf|}}) for your codes in the following problems. | ||
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* In your favorite programming language, make a program to construct a real symmetric $NxN$ matrix. Diagonalize it using the appropriate LAPACK or GSL routine, and write out some number of the lowest eigenvalues. (Suggestion: You might find it useful to use Mathematica (available on the ECT* computers) to diagonalize a small matrix that you can benchmark against.) This will help you test that you've linked to the GSL or LAPACK library. | * In your favorite programming language, make a program to construct a real symmetric $NxN$ matrix. Diagonalize it using the appropriate LAPACK or GSL routine, and write out some number of the lowest eigenvalues. (Suggestion: You might find it useful to use Mathematica (available on the ECT* computers) to diagonalize a small matrix that you can benchmark against.) This will help you test that you've linked to the GSL or LAPACK library. | ||
- | * Install Git, and try out some of the commands covered in Morten or Nicolas's lecture slides ({{:computing.pdf|}} {{:talentdftguides.pdf|}}) for your code in the first problem. | ||
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* The code {{:coulomboscrelme.f90.zip|}} calculates the relative matrix elements $\langle nl|V|n'l\rangle$ in HO states. From this, construct a subroutine that returns the properly normalized $r$-space HO wf's. For some basic background on HO wf's, see {{:ho_spherical.pdf| here}}. | * The code {{:coulomboscrelme.f90.zip|}} calculates the relative matrix elements $\langle nl|V|n'l\rangle$ in HO states. From this, construct a subroutine that returns the properly normalized $r$-space HO wf's. For some basic background on HO wf's, see {{:ho_spherical.pdf| here}}. | ||
- | * 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. | + | * 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. |
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+ | * 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 $b = \sqrt{(\hbar/(m\omega)}$. | ||
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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 | ||
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