PHYSICS 137A Final: physics137A-sp2016-final-Siddiqi-soln
Document Summary
137a spring 2016: siddiqi / e. dodds. Consider a three-dimensional vector space spanned by an orthonormal basis |1i ,|2i , and |3i. How are they related? (5 pts) (iii) find all nine matrix elements of the operator a = | ih | in the orthonormal basis |1i ,|2i , and |3i. Solution. (i) h | = ih1| 2h2| + ih3| and h | = ih1| + 2h3|. (ii) h | i = h | i = 1 + 2i. (iii) is not hermitian. Suppose a particle is in a potential that looks like v (x) = 1 energy and a0 is a characteristic length. 2 m 2x2 + v0 a0 x where v0 is a characteristic (i) write down the time-independent schr odinger equation (se). Se for the harmonic oscillator, but with an extra term. X2 (x) + [(m/2) 2x2 + (v0/a0)x] (x) = e (x). To eliminate the linear term, we can rewrite the potential as.
