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University of Cambridge/Numerical Answers to Tripos Questions/Natural Sciences Tripos/Physics A/2007 Paper 2

< University of Cambridge | Numerical Answers to Tripos Questions | Natural Sciences Tripos | Physics A

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Seaction AEdit

1.

2. 0.168 eV

3. \frac {n^2\pi ^2\hbar ^2}{2m\omega ^2}

4.

5. 8 levels -> need three bits. Sample at Twice bandwidth. 2x3x100=600

6.

section BEdit

7.

  1. Classical partical speeds up
  2. Terms mean kinetic + potential energy
  3. Boundary conditions: \psi continuous at x=0, \frac {d\psi }{dx} continuous at x=0
  4. General solutions: ??
  5. R=|r|^2=|\frac {k_1-k_2}{k_1+k_2} |^2
  6.  T=\frac {k_2}{k_1} |t|^2 =\frac {k_2}{k_1} |\frac {2k_1}{k_1+k_2} |^2
  7. sketch graph:
  8. R\approx 0, ??

8.

  1. constant of motion when [H,A]=0
  2. \frac {d<x>}{dt} =\frac {\langle p\rangle }{m} and \frac {d\langle p\rangle }{dt} = -\langle \frac {dV}{dx}\rangle = \langle F(x)\rangle

9.

???

10.

  1. Failed to parse (unknown function\math): \alpha =-\frac {ze^2m}{8\pi \alpha \epsilon \hbar ^2} <\math>,<math>E=-\frac {\alpha ^2\hbar ^2}{2m}

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