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Exam1key - Short Answer Questions: 1. Why does the...

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Unformatted text preview: Short Answer Questions: 1. Why does the existence of line spectra Violate classical physics? (4 pts.) , r (a) Write it and define all terms. (3 pts.) (0) Suppose you were scattering electrOns off a crystal. Coherent scattering requires the lattice constant (spacing) to be of the same magnitude as the wavelength. Show how the wavelength varies with the kinetic energy of a scattering particle. (4 pts.) ((1) Suppose a proton beam and an electron beam had the same energies such that 9L3 : 1 A. What ‘ would the wavelength of RP be? (Inp : 1836 me) (4 pts.) J6 fl ma _.___ [lg/{1% 41, _/m r‘ - 4—— Ep‘ EB (firle *' (8% Ea 3. Postulate 111 (my pestulates) states ‘P(X) and 9100/62: must be everywhere... (3 pts. each) (a) continuous: what does that mean? 7% (b) s'ngle valued: what does that mean? . x ‘ M flu ‘ 5L M “a” a“ 4W WWWQW 4. Consider a particle in the box with conditions V = 0, 0 <‘X < a and V = 00 elsewhere. In the box the Schrodinger equation can be written 62 2 ' Esra) =2—wa) (a) One possible set of solutions to this problem are the free particle-solutions ‘fl : Aefipxm and 1P" = Ae’jpx’” Show ‘l’+ is a solution to the Schrodinger equation. (3 pts.) agfwwxflw -/r (b) Does ‘l’+ obey the finite conditions ofPostulate III for a {seal particle? Why or why not? (4 pts.) _ i . E K/fi l6 n (PX - f .. "Z- r. as. *(fie we — a low Wefixlgogbé (c) On a physical basis why are ‘P+ and ‘P_ unlikely solutions to the particle in the box? (4 pts.) ’ _ kl,qu MwWWrLlfl-M‘Lxmfiw 1, p I , 30 WW ((4 pm [iii-Loam W Li; Mummy 3:) W is —W “W M (d) In cfis veal/Elena thi Lg- t9 £24m cm, below. (4 pts.) S \Piflioifi'l’qji): ilemrna by taking linear combinations of T+ and ‘1’“. Determine these J5 5K —T:KI‘ -LIA- {3 n+6 {my WW% J§ E if: = §r= X h D :9 H Yd q> 4/:me ‘9‘ 0 (g) What are the conditions on ~2— such that ‘1’; obeys Poiétulate III? (4 pts.) Sketches for We and in are givexbelow ‘ '- ‘P \o/l classical—turning points _ I _ 'classicaltuming points (a) When v = 0 the wave function has the form given'ab‘ove. Carefully draw {’02 and ‘1112 below. (4 pts.) 'y ..... / y classical turning points ' - classical tuming points —A : AI/LX (b) Is Axo > 0 for v = 0? Why or why not? (Hint: you don’t have calculate it just use arguments based on results above.) (3 pts.) 7 ' '\ A O ‘ , M - r @cégifla I Wm km) (c) What value" of Ape corresponds to Axo? (Hint: X and p do not commute for the Harmonic Oscillator.) (4 pts.) H p D AXAQZ’a/L Xitfil‘TMW ((1) At the classical turning point (V(y) = E), To is not zero. Write an expression that would allow you to calculate the probability that the particle exists in the forbidden zone (i.e., where V(y) > E) ' f =. . orv 0(40123ts) 41:08 ea 4‘01 30‘, éébpflaoo (i) the most time? :— O ' W, (Lil a M All, plagcéwocco (ii) the least time? % W (P503) (#005?) *jj O [W ' Give a brief justification for you answers. (f) For a classical Harmonic oscillator, like the pendulum, where does the oscillator spend... (4 pts.) ' (i) themosttime? - 1,: _ _ W) W 32$”m_ W W Give a brief justification for your answers. (g) State the correspondence principle. (3 pts.) - i " I _‘ / . (h) What must happen to ‘Pvz as v gets large? (3 pts.) ' EU: (KO-M2, (A190 L; wheat—eve / Eflaoo waQ " CJ . O “>5 H O l 00 Lil/O, glib. W (i) Determine the average value of y for ‘Pv(y). (Hint: rec l the properties of even and odd functions.) (4 pts.) ' (1') Determine the most probable values of y for v = 0 and V = 1.. (6 pts.) -WW “NP; :0 (h) The classical turning point is given by ytp: at: (2V + 1)”? Are your answers in part 0) consistent with the correspondence principle? Why or why not? (4 pts.) “at? [1710) 3 ( ...
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Exam1key - Short Answer Questions: 1. Why does the...

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