Problem_Set_2 - Chemistry 120A Spring Semester, 2009....

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Chemistry 120A Spring Semester, 2009. Problem Set 2 Due Fri. Feb. 6, 2009. 1. Another particle in a box problem. Suppose that a particle in a box (of length L ) is represented at an instant in time by a state ! with wavefunction: x ( ) = Nx 2 L 2 " x 2 ( ) (a) Evaluate the normalization constant, N , such that x ( ) is normalized (i.e. = 1 ) (b) Evaluate the average energy which would be obtained by making measurements on a very large number of identically prepared systems using the expectation value expression, E = ˆ H , for normalized wavefunctions. 2. A follow-on to “Another particle in a box problem”. Same particle in the same box, in the same state, : (a) A very natural basis in which to represent = " j c j j # is the basis of energy eigenfunctions, n where n is the quantum number. Evaluate the first few expansion coefficients ( c n =1 , c n =2 , c n =3 , c n =4 ) explicitly. (b)
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This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Head-gordon during the Spring '09 term at University of California, Berkeley.

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Problem_Set_2 - Chemistry 120A Spring Semester, 2009....

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