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ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on January 10, 2010, 06:48:55 AM

Title: GR9277.028
Post by: conantee on January 10, 2010, 06:48:55 AM

28. A system is known to be in the normalized state described by the wave function
$\psi (\theta, \phi) = \frac{1}{\sqrt{30}}(5Y_4^3+ Y_6^3 - 2 Y_6^0)$ ,
where $\Y_l^m (\theta, \phi)$ are spherical harmonics. The probability of finding the system in a state with azimuthal orbital quantum number $m=3$ is
(A) $0$
(B) $\frac{1}{15}$
(C) $\frac{1}{6}$
(D) $\frac{1}{3}$
(E) $\frac{13}{15}$

Title: Re: GR9277.028
Post by: gons on September 22, 2010, 08:04:05 PM

ตอบ (E) $\frac{13}{15}$

จาำก เอาสัมประสิทธ์หน้า $Y_{3}^{4}, Y_{6}^{3}$ มายกกำลังสองแล้วบวกกันจะได้ความน่าจะเป็น

Title: Re: GR9277.028
Post by: conantee on September 26, 2010, 02:32:04 AM

Correct. There is no trick in this question. This question just tests your knowledge about probability amplitude of wave function and orbital quantum number $m$ .

The probability of finding the system in a state with $m =3$ is $P = (\frac{5}{\sqrt{30}})^2$ (associated with $m=3$ ) $+ (\frac{1}{\sqrt{30}})^2$ (associated with $m=3$ ) $+ 0$ (not associated with $m=3$ ) $= \frac{25+1}{30} = \frac{13}{15}$

The correct answer is (E), and 59 of 100 people answer correctly.