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Уважаемые эксперты! Пожалуйста, ответьте на вопрос: На рисунке изображена плотность вероятности обнаружения микрочастицы на различных расстояниях от (стенок) потенциальной ямы . Вероятность ее обнаружения на участке???
График вероятности состоит из 2 "горбов", в участок [e/4;3e/4] попадает половина каждого горба. Поэтому Вероятность ее обнаружения = 1/2
Неизвестный
15.01.2012, 19:56
общий
это ответ
Здравствуйте, смирнов игорь! Предлагаю самый простой способ решения, графический: на исследуемом интервале заштрихуем исследуемую область и она рана 1/2 от всей области
Правильный ответ: вероятность обнаружения микрочастицы на данном участке равна W=1/2
Уравнение волновой функции для одномерной бесконечно глубокой ямы [$968$]=A[$183$]sin([$960$]nx/l) плотность распределения [$968$]2=A2sin2([$960$]nx/l)=0,5A2(1-cos(2[$960$]nx/l)) Учитывая что 0l[$8747$][$968$]2dx=0,5A2(x-(l/2[$960$]n)sin(2[$960$]nx/l))|0l=0,5A2l=1 получаем 0,5A2=1/l [$968$]2=(1/l)(1-cos(2[$960$]nx/l)) В данном случае n=2 (потому что 1-cos(2[$960$]nx/l) обращается в 0 в точках 0, l/2 и l) Интегрируем по указанному интервалу P=l/43l/4[$8747$][$968$]2dx=(1/l)(x-(l/4[$960$])sin(4[$960$]x/l))|l/43l/4= =(1/l)(3l/4-(l/4[$960$])sin(3[$960$]))-(1/l)(l/4-(l/4[$960$])sin([$960$]))=(1/l)(3l/4-l/4)=1/2
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