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liboff : ¾çÀÚ¿ªÇÐ 2ÆÇ ¼Ö·ç¼Ç (ÀúÀÚ Liboff 2nd ed Introductory Quantum Mechanics)

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[¼Ö·ç¼Ç] ¾çÀÚ¿ªÇÐ 2ÆÇ (ÀúÀÚ Liboff 2nd ed - Introductory Quantum Mechanics) ¼Ö·ç¼Ç ÀÔ´Ï´Ù.

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March 1, 2007
7.35 The wavefunction that we are given depends only on x and t. So the only nonzero component of J will be Jx . We are given: ¥÷(x, t) = Aei¥õ(x,t) , where ¥õ(x, t) is real. Use equation (7.106) in Libo? to ?nd: Jx = h ? ¡Ó¥÷ ? ¡Ó¥÷ ¥÷? ?¥÷ 2mi ¡Óx ¡Óx

=

h ? 2mi

A? e?i¥õ(x,t)

Aiei¥õ(x,t)

¡Ó¥õ ¡Óx

? Aei¥õ(x,t)

A? (?i)e?i¥õ(x,t)

¡Ó¥õ ¡Óx

=

h ? ¡Ó¥õ |A|2 . m ¡Óx

7.38 a.According to Eq. (7.107), J= h ? ¥÷? ¥÷ ? ¥÷ ¥÷? . 2mi

If ¥÷ is real, we have ¥÷ ? = ¥÷, and then clearly J = 0. b.From the continuity equation (equation (7.105) in Libo?), J = 0 implies ¡Ó¥ñ ¡Ót = 0, where ¥ñ is the probability density or alternatively the particle density in scattering problems. So, we see that a real state function implies that the probability density (aka particle density) remains constant.

1

Ph12b Solutions

Problem Set 7

March 1, 2007

7.41 Consider the two con?gurations in Figure 7.21. Libo? has calculated the re?e



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