PHYSICS 137A Midterm: physics137A-sp2006-mt1--exam
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Two sides of your own notes are allowed. No books or calculators are allowed, and please ask for help only if a question"s meaning is unclear: consider the harmonic oscillator ground state wavefunction (x) = ae m x2/2 h with a = H (cid:1)1/4, which makes this a normalized wavefunction. (cid:0) m . For this problem, you may wish to use the gaussian integrals. 4a3 . (1) (a) (5 points) write an integral for the probability to nd the particle between x = b and x = c. Try at least to write an integral; do the integral if you can: at t = 0, suppose that a state in the in nite square well with potential. V (x) = (cid:26) if x < 0 or x > a. 0 has the wavefunction if 0 x a. 2 where the normalized eigenstates are n = q 2 a sin(n x/a).
