PHYSICS 137A Midterm: physics137A-sp2014-mt2-Markov-soln
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Problem 1 sequential measurements (modified griffiths problem 3. 27) An operator a, corresponding to an observable , has two normalized eigenstates | 1i and | 2i, with eigenvalues a1 and a2. An operator b, corresponding to another observable , has two normalized eigenstates | 1i and | 2i, with eigenvalues b1 and b2. A observable is measured and value b1 is obtained. Problem 2 harmonic oscillator vs hydrogen atom ground state. A show that 0(r) e ar2. B show that 1(r) e br is a solution of the schr odinger equation for the hydrogen atom, provided that. Normalize the wave function. is a solution of the schr odinger equation for the harmonic oscillator, provided that a = m . C if we move along, say, the x-axis, there is a kink (a discontinuity in slope) in the hydrogen atom ground state. A hydrogen atom is in its ground state just like in problem 2 b.
