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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
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