Unformatted text preview: x 2 /a 2 ) 2 dx = A 2 Z ∞∞ ( ex 2 /a 2 ) 2 dx = A 2 a r π 2 = A 2 r πa 2 2 (2) and we must then have A 2 = r 2 πa 2 , so that A = h 2 πa 2 i 1 / 4 . (3) b) The speciﬁed interval (from0.1 nm to +0.1 nm) is much smaller than the range over which the exponential varies appreciably (which is on the order of a = 1.5 nm). Therefore, the wavefunction may be taken to be constant across that small interval (equal to its value at x = 0) and removed from the integral. We then have Probability = Z +0 . 1 nm. 1 nm  ψ ( x )  2 dx ≈  ψ (0)  2 Z +0 . 1 nm. 1 nm dx = A 2 × 2(0 . 1 nm) = r 2 πa 2 × 2(0 . 1 nm) = r 2 π 1 . 5 2 × 2(0 . 1) = 0 . 1064 . (4) 1...
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 Spring '11
 EricSzarmes
 Physics, Work, Square wave, Equals sign, Sine wave, 0 l, 0 1 3L

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