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[ÆÇ¸ÅÁßÁö] ±¸¸Åȸ¿ø¿äû ÆÇ¸ÅÁßÁö(»çÀ¯) : Liboff Ã¥À» Áߺ¹½ÅûÇß½À´Ï´Ù. ±×¸®°í ±ÛÀÚµµ Á¶¾ÇÇØ¼­ µµÀúÈ÷ ¾Ë¾Æº¼¼ö°¡ ¾ø³×¿ä. -------> [¼Ö·ç¼Ç] ¾çÀÚ¿ªÇÐ 2ÆÇ (ÀúÀÚ Liboff 2nd ed - Introductory Quantum Mechanics) ¼Ö·ç¼Ç ÀÔ´Ï´Ù. ÃÑ 1ÀåºÎÅÍ 13Àå±îÁöÀÇ ¼Ö·ç¼ÇÀ¸·Î ±¸¼ºµÇ¾î ÀÖ½À´Ï´Ù. °øºÎ ÇÒ ¶§ Á¤¸» µµ¿òÀÌ ¸¹ÀÌ ‰ç´ø ÀÚ·á ÀÔ´Ï´Ù. ¿¹½ÀÇÒ¶§³ª, º¹½ÀÇÒ¶§³ª ±×¸®°í ½ÃÇè±â°£¿¡ ƯÈ÷ ²À ÇÊ¿äÇÑ ÀÚ·áÀÔ´Ï´Ù..^^
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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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Ph12b Solution Set 7
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) ¡ë Aei¥õ(x,t) , where ¥õ(x, t) is real. Use equation (7.106) in Libo? to ?nd: Jx ¡ë h ? ¡Ó¥÷ ? ¡Ó¥÷ ¥÷? ?¥÷ 2mi ¡Óx ¡Óx

¡ë

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

¡ë

h ? ¡Ó¥õ |A|2 . m ¡Óx

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

If ¥÷ is real, we have ¥÷ ? ¡ë ¥÷, and then clearly J ¡ë 0. b.From the continuity equation (equation (7.105) in Libo?), J ¡ë 0 implies ¡Ó¥ñ ¡Ót ¡ë 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¡¦(»ý·«)



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