1. (a) Consider the 1s level of a hydrogen atom and also the 2p level with m = 0
ID: 1998775 • Letter: 1
Question
1. (a) Consider the 1s level of a hydrogen atom and also the 2p level with m = 0. In the Hilbert space with these two levels as basis vectors, write the matrix for the operator z. (b) What is the expectation value of the hydrogen atom Hamiltonian for any equalweight superposition of these two levels? (Equal-weight superposition means that the magnitudes of the two expansion coefficients are the same.) Hint: the 1s level by itself has energy 13.6eV . (c) Out of all equal-weight superpositions of these two levels, find the one that has the maximum possible expectation value of z. (d) Let the state in (c) be the state of the system at time t = 0. At what time will the expectation value of z have reversed (same magnitude but opposite sign)? (You can guess even if you weren’t able to solve (c)).
Explanation / Answer
http://titan.physx.u-szeged.hu/~benedict/BM_At_Mol_Light.pdf
http://isites.harvard.edu/fs/docs/icb.topic1294838.files/285b_notes_2005-1.Lily.pdf
http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory%20Concepts%20and%20Methods.pdf
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