Fall 07 Phys 143l Exam 2 Soultions

Fall 07 Phys 143l Exam 2 Soultions - Duke University...

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Unformatted text preview: Duke University Department of Physics Physics 143 Fall Term 2007 QEEZ 2 4» I will abide by the Duke Community Standard. Name: This is a closed book quiz, with one side of one page cheat sheet allowed. Calculators are allowed, but only for basic calculations: you may not use special memory, graphing etc. functions. You must always show your work for credit. You must hand in your cheat sheet with your test. This quiz has eight problems, each worth 10 points. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Total Problem 1: The longest wavelength line in the spectrum emitted by an electron trapped in an infinitely deep square well is 690 nm. What is the Width of the well? («0&365‘7 wme «5 I w far {A TOW/Wen? M 0; 0:3,“) ,m m :2 Q 5f 2:" E AE 7— : z {F W Z t A «a; 5:2” \“ZV/l "ELM if“ Problem 2: Consider the wavefunction what) = fiWfifle‘iEfi/h + ’U3($)€‘iE3t/h)x Write an expression for the probability that the electron is in the range between :I: = L/ 2 and :1: = L, as a function of time. (You do not need to evaluate this expression.) / R “my, Problem 3: An atom in the n z 2 state of hydrogen remains there on average about 10 ms before jumping to the n = 1 state. Estimate the uncertainty in the energy of the n z 2 state. What fraction of the transition energy is this? ‘ "3W .~ r” " [‘OS XIQ 3;» gyg,‘ Urge A g ’v is,” w LWWWW WWW W - S. a a Q j :4. A i; t “,7 “MW...”wa Z“ “i; l (m x I C.) J ‘— évflp =33}st Trans! :5 o n V1 2 La») mm. % f I - a fig /y.»rgteétxam ta E x 104 3 x (O in V 22; m Problem 4: Explain What is meant by a “central potentia ”. Give two examples of a force associated with a central potential. Write down the 3D Schrodinger equation (in any coordinates) for a central potential7 identifying the kinetic and potential energy components of the Hamiltonian. mm Q «m Problem 5: For a given magnitude of L = x/l(l + 1)h of 5, what is the largest allowed value of Lz? [/21 ES Ma 91 \ffixm“ {so ’Hm Problem 6: Sketch an approximate 1D potential representing a scanning tunneling microscope tip and metal surface, noting all relevant features. How and Why does the current vary as the tip’s distance 2 from the surface changes? {‘7 \ V? Problem 7: Consider a wavefunction of the form Was, t) = Aei(Pm"Et)/h. What is the physical interpretation of this wavefunetion? If you were to measure the momentum for a particle described by this wavefunction7 What would be the spread? What about a measurement of energy? What about a measurement of position? V? «a. Z? roblem 8: Consider a triangular potential as shown in the figure. Write an ex~ pression for Write an approximate expression for the transmission probability for an electron with E << A. ‘ V r" V(x) 9 M FM“ a aw I ~\/\E 2“” A i a. \ % * “2:” O a W», W N ‘ ,/ ...
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Fall 07 Phys 143l Exam 2 Soultions - Duke University...

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