PracticeQuestionsFor1stMidterm - Chem 113A Practice...

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Chem 113A Practice Questions for 1 st Midterm The following questions are intended as general practice for the 1 st midterm assessment and will not be collected or graded. Solutions will not be posted. If you have questions about solutions, please speak wi th the lecturer or either of the TA’s 1) What is the general solution to linear differential equations with constant coefficients? 2) Suppose a particle of mass ? = 1.67 × 10 −27 kg is contained in a 1-dimensional box of length 𝐿 = 3 Å. The particle is in an eigenstate of the Hamiltonian such that its wavelength is 0.4 Å. a. What is the translational energy of the particle? b. What is the magnitude of the particle’s momen tum? 3) For a particle of mass ? , in a 1-D box of length 𝐿 , in an energy eigenstate 𝜓 ? : a. Determine the uncertainty in the position of the particle b. Determine the uncertainty in the momentum of the particle. c. For which eigenstate 𝜓 ? is the product of the uncertainties in position and momentum at a minimum?
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