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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.