University of California Hooks Law Force & GS of Macroscopic HO Problem 6

University of California San Diego

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Problem 6.3.1 : GS of macroscopic HO u A harmonic oscillator has a Hook’s law force constant k=25 N/m and has a mass of 1 gram. What is the ground state energy? A. B. C. D. E. 5.18 X 10-14 J 8.30 X 10-33 J 1.31 X 10-30 J 2.62 X 10-30 J 1.97 X 10-22 J k ω= m 1 Problem 6.3.2: Expected x in HO u What is the expected value of x in the first excited state of the HO? A. 2! mω B. ! 2mω C. ⎛ mω ⎞ u1 = ⎜ ⎟ ⎝ π! ⎠ 1 4 −mω x 2 2mω 2! x e ( ) ! 1 D. ! mω E. 0 2 Problem LQ6.4.1: Potential Step u A beam of 5 eV electrons is incident upon a potential step of height 3 eV. What is the probability to be transmitted? A. B. C. D. E. 1.44 0.225 0.051 0.949 0.775 1 Question LQ6.4.2: Potential Barrier u Tunneling is an important in transistors, amplifiers. If one adjusts the potential in the classically forbidden region for a potential barrier, approximately how does the transmission probability depend on the (gate) voltage? A. B. C. D. E. There are some discreet voltages with 100% transmission It is linear in the barrier voltage It is independent of the barrier voltage It falls off exponentially in the barrier voltage We cannot tell from the information given 2 ...
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