p40_017 - 17. The probability that the electron is found in...

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17. The probability that the electron is found in any interval is given by P = R | ψ | 2 dx , where the integral is over the interval. If the interval width ∆ x is small, the probability can be approximated by P = | ψ | 2 x , where the wave function is evaluated for the center of the interval, say. For an electron trapped in an in±nite well of width L , the ground state probability density is | ψ | 2 = 2 L sin 2 ³ πx L ´ , so P = µ 2∆ x L sin 2 ³ πx L ´ . (a) We take L = 100 pm,
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