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Консультация № 198126
02.04.2020, 20:19
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Здравствуйте! У меня возникли сложности с таким вопросом:
Частица находится в одномерной прямоугольной "потенциальной яме" с бесконечно высокими "стенками". Ширина ямы - l. Состояние частицы описывается главным квантовым числом n. Определить: 1) вероятность нахождения частицы в области "ямы" l = x2-x1 ; 2) точки интервала [х1,х2], в которых плотность вероятности существования частицы максимальна и минимальна. n=2, x1=0,7 , x2=0,9 .
Частица находится в одномерной прямоугольной "потенциальной яме" с бесконечно высокими "стенками". Ширина ямы - l. Состояние частицы описывается главным квантовым числом n. Определить: 1) вероятность нахождения частицы в области "ямы" l = x2-x1 ; 2) точки интервала [х1,х2], в которых плотность вероятности существования частицы максимальна и минимальна. n=2, x1=0,7 , x2=0,9 .
Обсуждение
07.04.2020, 19:16
общий
это ответ
Здравствуйте, fm11!
Плотность вероятности нахождения частицы в конкретной точке определяется величиной |[$968$]|[sup]2[/sup], где [$968$] - волновая функция, которая для частицы, находящейся в одномерной прямоугольной "потенциальной яме" шириной l в возбуждённом состоянии с главным квантовым числом n, имеет вид
Соответственно, вероятность нахождения частицы в интервале [x[sub]1[/sub], x[sub]2[/sub]] будет равна
В данном случае для x[sub]1[/sub] = 0.7l, x[sub]2[/sub] = 0.9l и n = 2 имеем
Соответствующая функция плотности вероятности
имеет максимум, равный 2/l, при x = l/4, 3l/4 и минимум, равный 0, при x = 0, l/2, l. В интервал [0.7l, 0.9l] попадает точка максимума x = 3l/4, а на краях интервала плотность вероятности равна
и
то есть плотность вероятности минимальна при x = 0.9l.
Плотность вероятности нахождения частицы в конкретной точке определяется величиной |[$968$]|[sup]2[/sup], где [$968$] - волновая функция, которая для частицы, находящейся в одномерной прямоугольной "потенциальной яме" шириной l в возбуждённом состоянии с главным квантовым числом n, имеет вид
Соответственно, вероятность нахождения частицы в интервале [x[sub]1[/sub], x[sub]2[/sub]] будет равна
В данном случае для x[sub]1[/sub] = 0.7l, x[sub]2[/sub] = 0.9l и n = 2 имеем
Соответствующая функция плотности вероятности
имеет максимум, равный 2/l, при x = l/4, 3l/4 и минимум, равный 0, при x = 0, l/2, l. В интервал [0.7l, 0.9l] попадает точка максимума x = 3l/4, а на краях интервала плотность вероятности равна
и
то есть плотность вероятности минимальна при x = 0.9l.
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