SAMPLING TECHNIQUE PSTAT 123
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This 4 page Class Notes was uploaded by Douglas Simonis on Thursday October 22, 2015. The Class Notes belongs to PSTAT 123 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 88 views. For similar materials see /class/226916/pstat-123-university-of-california-santa-barbara in Statistics and Probability at University of California Santa Barbara.
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Date Created: 10/22/15
University of California Santa Barbara Department of Physics Physics 123A CONDENSED MATTER PHYSICS FALL 2008 Prof Paul Hansma Supplementary Problems from David Vanderbilt Rutgers 1a For the twodimensional elemental crystal shown below do the atom positions form a lattice How many atoms are in the primitive cell Specify the lattice vectors 39139 and 5 sketch the unit cell and give the unit cell area 0 00000O o o ooogo ul ooocg poo 39l b For the twodimensional compound shown below composed of atoms of type A and B how many atoms are there per primitive unit cell Specify a set of primitive lattice vectors sketch the primitive unit cell and give the primitive cell area Lt 0006000 90000000 090009000 L2 c For the same structure as in b choose a set of conventional lattice vectors such that 515 How many atoms are there per conventional cell What is the conventional cell area 2 Express the following in eV a Energy to remove an electron from a hydrogen atom b Boltzmann energy kT for T TRoom 273 K c 1 kcalmole a Common unit in chemistry d Cohesive energy of Xe e Cohesive energy of Si f Approximate energy of a visible light photon g Approximate energy of an Xray photon 3a A typical solid has a lattice constant a 4121 and sound velocity v 105 cms Use the dispersion relation from the continuum wave equation 0 vk to estimate the frequency of a phonon at the edge of the Brillouin zone k 1ra b Calculate the related energy quantum E fun and convert it to electron volts c Suppose this crystal is held at very low temperature in vacuum with one atomic mono layer of neon atoms bound to the surface by Van der Waals interactions Suppose 002 eV is required to eject a single neon atom from the surface Is it possible that a phonon arriVing at the surface can cause the ejection of a neon atom 4 Review the discussion in Kittel of the behavior of electrons in the presence of a magnetic eld pp 147 8 a Using Eq 52 discuss what happens when the magnetic eld B is along the 2 axis and the electric eld E is along the 5 axis Show that in this case the drift velocity 17 is not parallel to the applied E eld instead it lies in the xy plane at an angle 9 from the x axis Write an expression for 0 in terms of we and T b As you increase the Bfield does the angle increase or decrease c As you increase the temperature does the angle increase or dectease 5 Do either one of the following a Kittel problem 73 KronigPenney model Recall cosx 1 x22 sinI 1 x36 i b Write a computer program to solve the Kronigpenney model for the case of the periodic deltafunction potential with P 37r2 as in Fig 75 Take a 1 and hZm 1 for simplicity Generate a plot which shows 6k for the rst band or two for 0 S k S 7ra ie in the reduced zone scheme I have in mind that you do this by running over a mesh of values of energy say from D to 30 For each energy look for a solution of Eq 721b if there is a solution put a point on the plot You do not have toiconnect the points on the plot by lines Once you have the program working see what the solution looks like if you decrease the value of P or change its sign Hintz When you change sign you will need to include also some negative energies You may need to use sint L sinh lt15 and cos 13 cosh 4 of t 3 Annaidix 011 UniA 1115 Dimensions t Table 3 Conversion tabie for symbols and formulas The symbols for mass length time force and other 39not speci cally electro magnetic quantities are unchanged To convert any equation in Gaussian variables to the corresponding equation in mks quantities on both sides of the equation replace the relevant symbols listed below under quotGaussianquot by the corresponding mks symbols listed on the right The reverse transformation is also allowed Since the length and time symbols are unchanged quantities which differ dimensionally from one another only by powers of length andor time are grouped together where possible Quantity Gaussian mks Velocity of light c toe or xi Electric eld Em V Wis 6 mo V potential voltage 4n Displacement D 1 ME I o 1 Charge density charge current density pq J I P 349 J I P current polarization 47750 A 417 Magnetic induction B A B 0 Magnetic eld H 141rizo H M1 netization M M 5 4quot C d O on uctiVIty 0 27760 6 Dielectric constant e 0 Permeability u 0 Resistance impedance RZ 417 0RZ Inductance L 4760L 1 Capacitance C 47750
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