Chỉ khi nào hai toán tử
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)
và
giao hoán với nhau tức là thỏa mãn
![](data:image/png;base64,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)
thì hai đại lượng vật lí tương ứng
A, B mới có thể xác định được chính xác đồng thời.
Bài 16: Chứng minh rằng không thể xác định đồng thời chính xác ví trí và động lượng của một hạt bất kì.
Giải
Ta xét
Kết luận: Hai toán tử vị trí và động lượng không giao hoán nên vị trí và động lượng không thể xác định chính xác đồng thời (nguyên lý bất định Heisenberg).
III. KHẢ NĂNG ÁP DỤNG CỦA GIẢI PHÁP
Đưa ra những kiến thức cơ bản và cơ sở phù hợp với công cụ toán học hiện có của học sinh phổ thông nhằm giúp các em đọc có thể hiểu và có hiểu biết đầu tiên về vật lí lượng tử. Thông qua đó bổ trợ kiến thức và công cụ toán cho giảng dạy phần vật lí hiện đại và vật lí hạt nhân. Áp dụng là một số bài toán khó trong các kì thi chọn học sinh giỏi THPT Quốc gia, Quốc tế.
Đề tài này sẽ hệ thống lại những kiến thức cơ bản nhất của “Cơ sở vật lí lượng tử”. Sau mỗi phần lí thuyết đều có các bài tập ví dụ với lời giải cụ thể. Phần cuối là các bài tập được lấy ra từ các đề thi Olymlic, đề thi học sinh giỏi quốc gia để học sinh tự luyện tập chuẩn bị cho các kì thi học sinh giỏi sắp tới.
IV. HIỆU QUẢ, LỢI ÍCH THU ĐƯỢC
Chuyên đề “Cơ sở vật lí lượng tử” được viết ra để tổng hợp, hệ thống lại lý thuyết cùng các bài tập vận dụng nhằm giúp học sinh tháo gỡ khó khăn khi học phần kiến thức này và để học sinh có thể ngang tầm khu vực, quốc tế từ đó đạt các giải cao trong kì thi học sinh giỏi quốc gia, quốc tế.
Năm 2016 đội tuyển học sinh giỏi quốc gia môn Vật lí của tỉnh Điện Biên có học sinh đạt giải ba. Năm 2017 đội tuyển học sinh giỏi quốc gia môn Vật lí của tỉnh Điện Biên có học sinh đạt giải nhì.
V. PHẠM VI ẢNH HƯỞNG CỦA GIẢI PHÁP
Nội dung đề tài được trích từ các chuyên đề mà chúng tôi đã dùng để giảng dạy cho học sinh trong các lớp chuyên lý và học sinh các đội tuyển HSG của tỉnh tham dự kì thi HSG quốc gia môn vật lý và các học sinh tham dự Olympic Vật lý quốc tế với mục tiêu là giúp học sinh có cách nhìn tổng quát nhất về lý thuyết “Cơ sở vật lí lượng tử” dựa trên việc xây dựng hệ thống lý thuyết cơ bản. Vận dụng giải và phân tích các bài toán trong chương trình thi HSG quốc gia, quốc tế tại trường THPT chuyên Lê Quý Đôn. Từ đó nâng cao về chất lượng giải học sinh giỏi quốc gia môn Vật lí.
VI. KIẾN NGHỊ, ĐỀ XUẤT
Qua thời gian nghiên cứu và giảng dạy tôi thấy rằng việc xây dựng các nội dung lý thuyết vật lý bằng những giả thuyết và công cụ toán học. Phân tích các kết quả tìm được là một giải pháp tốt để giúp học sinh nắm bắt các quá trình diễn biến của hiện tượng. Làm cho các em hiểu và nhớ được nội dung, kiến thức một cách sâu sắc hơn.
Việc xây dựng các nội dung lý thuyết vật lý bằng những giả thuyết và công cụ toán học cũng đã khắc phục được sự thiếu thốn và chưa đồng bộ được thiết bị thí nghiệm, đồng thời cũng khắc phục được sự hạn chế về năng lực thí nghiệm của giáo viên trong khi các đơn vị chưa có cán bộ thiết bị, chưa đảm bảo được kĩ thuật lắp ráp và tiến hành các thí nghiệm lẫn phương pháp sử dụng các thí nghiệm đó trong giờ học sao cho tăng cường được hoạt động nhận thức tự chủ, sáng tạo của học sinh.
Tôi xin chân thành cảm ơn!
Phần IV. TÀI LIỆU THAM KHẢO
[1]. Bài tập vật lí lý thuyết – Nguyễn Hữu Mình, Đỗ ĐìnhThanh - Nhà xuất bản giáo dục 2009
[2]. Giáo trình cơ học lượng tử - Lê Viết Hòa- ĐHSP Hà Nội
[3]. Giáo trình cơ học lượng tử - Ths Nguyễn Duy Hưng.
[4]. Cơ học lượng tử - Tập 1- Phạm Quý Tư, Đỗ ĐìnhThanh - ĐHSP Hà Nội