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Unformatted text preview: Chemistry 120A, Spring 2009 Midterm 2 Solutions March 20, 2009 Problems Problem 1: Multiple choice problems: 7 3 = 21 points 1. Linear combination of solutions to the time-dependent Schr odinger equation are solutions of the time-dependent Schr odinger equation: (a) always (b) sometimes (c) never A 2. Linear combination of solutions to the time-independent Schr odinger equation are solutions of the time-independent Schr odinger equation. (a) always (b) sometimes (c) never B 3. As the force constant k associated witha diatomic molecule is increased, the uncertainty in the momentum in the vibrational ground state will: (a) increase (b) decrease (c) stay the same A 4. How do you expect the wavelength of the n = 1 to n = 2 transition in the H atom to compare with the same transition in the He + atom? (a) longer in H (b) longer in He + (c) same A 5. Is it possible to simultaneously know the total value of angular momentum and its component along the x axis? (a) always (b) sometimes (c) never A 6. In the linear variational method, can an approximated ground state energy be below the true ground state energy? (a) always (b) sometimes (c) never C 7. What is the symmetry of this spin wavefunction with respect to particle interchange? (1 , 2) = (1) (2)- (1) (2) (a) symmetric (b) antisymmetric (c) neither B 1 Problem 2 (20 Points): Perturbartion theroy: You know the soltuions to the problem: H (0) (0) m E = E (0) m (0) m E and you are going to try to solve for the eigenvalues and eigenvectors of a related problem: H (0) m E = E m (0) m E where the difference between the two problems is called the perturbation: H = H (0) + V (1) and the strength of the perturbation is measured by some parameter . (a) (8 points) By writing power series expanstions in for the eigenvalues and eigenvectors, derive an expression for the leading correction to the eigenvalues of the solved problem due to the presence of the perturbation....
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- Spring '09