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Консультация № 190914
23.04.2017, 22:28
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Микрочастица находится в одномерной бесконечно глубокой потенциальной яме шириной ℓ, имея минимальную
энергию. Во сколько раз отличаются вероятности обнаружения частицы на отрезке шириной ℓ/4, если этот
отрезок лежит: 1. В середине ямы, 2. На краю ямы? Поясните смысл полученного результата графически
Заранее благодарен!С уважением!
Микрочастица находится в одномерной бесконечно глубокой потенциальной яме шириной ℓ, имея минимальную
энергию. Во сколько раз отличаются вероятности обнаружения частицы на отрезке шириной ℓ/4, если этот
отрезок лежит: 1. В середине ямы, 2. На краю ямы? Поясните смысл полученного результата графически
Заранее благодарен!С уважением!
Обсуждение
30.04.2017, 09:22
общий
это ответ
Здравствуйте, r-zaynullin!
Запишем волновую функцию, соответствующую минимальной энергии частицы, то есть при
Вероятность нахождения частицы можно вычислить по формуле
Заметим, что
(постоянную интегрирования опускаем), и получим
вероятность нахождения частицы на отрезке шириной
если этот отрезок лежит в середине ямы, то есть при 
вероятность нахождения частицы на отрезке шириной если этот отрезок лежит на левом краю ямы, то есть при 
вероятность нахождения частицы на отрезке шириной если этот отрезок лежит на правом краю ямы, то есть при 
Для графической интерпретации полученных результатов воспользуемся схематичным графиком функции
для 
показанным на рисунке ниже.
Вероятность
пропорциональна площади, окрашенной в синий цвет, вероятность 
пропорциональна площади, окрашенной в красный цвет, вероятность 
пропорциональна площади, окрашенной в зелёный цвет, если считать площадь всего графика пропорциональной единице.
Запишем волновую функцию, соответствующую минимальной энергии частицы, то есть при
Вероятность нахождения частицы можно вычислить по формуле
Заметим, что
(постоянную интегрирования опускаем), и получим
вероятность нахождения частицы на отрезке шириной
если этот отрезок лежит в середине ямы, то есть при вероятность нахождения частицы на отрезке шириной
если этот отрезок лежит на левом краю ямы, то есть при вероятность нахождения частицы на отрезке шириной
если этот отрезок лежит на правом краю ямы, то есть при Для графической интерпретации полученных результатов воспользуемся схематичным графиком функции
для показанным на рисунке ниже.Вероятность
пропорциональна площади, окрашенной в синий цвет, вероятность пропорциональна площади, окрашенной в красный цвет, вероятность пропорциональна площади, окрашенной в зелёный цвет, если считать площадь всего графика пропорциональной единице.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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