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ProblemSet2

# ProblemSet2 - Chem 120A Problem Set 2 Out Due 1 a If A is...

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Chem 120A Problem Set 2 Out: February 14, 2006; Due: February 22, 2006 1. a) If A is an operator with A ± ± α ² ³ β ± ± , prove that A = ± ± β ² ³ α ± ± . b) Show that the product of two Hermitian operators need not be Hermitian. Under what condition is the product of two Hermitian operators Hermitian? 2. The energy di±erence between the ground state (lowest energy level) and ²rst excited state (next level up) in a hydrogen atom is about 10 eV (eV = electron volt). The diameter of a hydrogen atom is 1 ˚ A= 10 - 10 m. If we model a hydrogen atom as a 1-D box with hard walls, then what is the length of the box to get the same energy level spacing as hydrogen? 3. Consider a particle of mass = m sitting in the ground state of a box of length=l. Suppose that one wall of the box is suddenly moved out so that the length of the box becomes length = 3l. a) If the energy of the particle is measured right after moving the wall, then what is the probability that the particle with be found in the n=10 state of the new box? b) How does this probability change with time?

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ProblemSet2 - Chem 120A Problem Set 2 Out Due 1 a If A is...

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