Question

uion or the for a particle in a box in a state described in the previous problem. Plot your result through one cycle. blem, we shall develop the consequence of measuring the position of a particle 4-42. In this box. If we find that the particle is located between a/2-/2 and a/2+/2, then its wave function may be ideally represented by a/2 - /2 <x <a/2+/2 x > a/2+/2 Plot ?(x) and show that it is normalized. The parameter e is in a sense a gauge of the accuracy of the measurement; the smaller the value of e, the more a Now let's suppose we measure the energy of the particle. The probability that we observe the value E, is given by the value of I crl2 in the expansion ccurate the measurement. where 1.'n(x) (2/a) 1 2 sin nmx/a and E-n2h2/8ma2. Multiply both sides ofthis equa tion by m(x) and integrate over x from 0 to a to get 2a Now show that the probability of observing En is given by if n is even p(En)asin TE if n is odd 2a ot p(En) against n for e/a-0.10, 0.050, and 0.010. Interpret the result in terms of the uncertainty principle. 4-43. Starting with and the time -dependent Schrödinger equation, show that

#4-42

Quantum Chemistry- McQuarrie 2nd edition

Answer 1

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Y1 2 Sin n -; y= {.1, .05, .01); Table [ Plot [ply[ [i]]], {n, 1, 11), AxesLabe1 → {"y", p}], {i, 1, 3}] 0.005 0.01 0.0 0.01 0.0 0.0 0.00 4 6 8 10 4 6 8 10 4 6 8 10 Particleis localized for even values on n