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Material Type: Exam; Class: INTRO MODERN PHYSICS; Subject: Physics & Astronomy; University: University of Louisville; Term: Unknown 1989;
Typology: Exams
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Mid-Term Exam 2 - PHYS 300 - Modern Physics Mendes, Spring 2009, March 24, 2009 Start time: 11:00 a.m. End time: 12:15 am Open textbook, notes, homeworks, and quizzes Calculators allowed; no other electronic device allowed Where it is appropriate, make sure to provide physical units to your numerical answer
(30 points)
a) Treating this as a one-dimensional infinite-square-well potential, calculate the approximate value of the quantum number n associated with the corresponding energy level.
b) What is the relative energy difference, defined by ⎛⎜⎝^ En^^ +^1 E − nEn ⎞⎟⎠ , between two adjacent states for a particle in an infinite-square-well potential?
c) For the specific value ofbetween the predictions of quantum mechanics for discrete energy levels and the n you calculated above , do you expect significant changes predictions of Newtonian physics for continuous energy levels. Justify your answer.
(40 points)
a) Using Schrodinger approach, compute the energy of the electron in this particular state. Does this result agree with Bohr’s model? Explain your answer.
b) Using Schrodinger approach, compute the magnitude of the angular momentumDoes this result agree with Bohr’s model? Explain your answer. L.
c) Compute all the possible values of Lz of this physical situation.
d) Choose one particular value of Lz (i.e., one value of m ) and write down the complete wavefunction (as a function of the spherical coordinates r , θ , f and time t ) for this quantum state of the electron in the hydrogen atom. Do not worry about normalizing your wavefunction.
