computer-assignment-3 - Chem. 540, Fall 2010 Instructor:...

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Chem. 540, Fall 2010 Instructor: Nancy Makri Computer Assignment 3 Eigenstates of General Hamiltonians in 1d In this assignment you will calculate energy eigenvalues using a symbolic algebra program, but this time the Hamiltonian matrix is not readily available. You will have to choose a basis set and evaluate the matrix elements by performing the integrals. The system is a particle of mass 1 m = in a potential ( ) V x (to be specified below). Thus, the Hamiltonian has the form 2 ˆ ˆ ˆ ( ) 2 p H V x m = + . Your goal is to calculate the five lowest energy eigenfunctions and eigenvalues with accuracy of 0.1% in the energies. For convenience I suggest using particle-in-a-box basis functions. You should do this for two potentials, (i) 2 1 2 ( ) V x x = and (ii) 4 1 2 ( ) V x x = . I recommend you write the program with the harmonic potential in mind, in which case you know the answers, so you can check things. Once everything is ok, you could copy the program and replace the potential
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computer-assignment-3 - Chem. 540, Fall 2010 Instructor:...

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