Задача №46.16
Условие
Собственная функция, описывающая состояние частицы в потенциальном ящике, имеет вид ψn(x)=Csin(πnx/l). Используя условия нормировки, определить постоянную C.Решение
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1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.49
1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
2.56
2.57
2.58
2.59
2.60
2.61
2.62
2.63
2.64
2.65
2.66
2.67
2.68
2.69
2.70
2.71
2.72
2.73
2.74
2.75
2.76
2.77
2.78
2.79
2.80
2.83
2.84
2.85
2.86
2.87
2.88
2.89
2.90
2.91
2.92
3.1
3.2
3.3
3.4
3.6
3.7
3.8
3.11
3.12
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
3.30
3.31
3.32
3.33
3.34
3.35
3.36
3.37
3.38
3.39
3.40
3.41
3.42
3.43
3.44
3.45
3.46
3.47
3.48
3.49
3.50
3.51
3.52
3.53
3.54
3.55
3.56
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.25
4.26
4.27
4.28
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.49
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.59
4.60
4.61
4.62
4.63
4.64
4.65
4.66
5.1
5.3
5.4
5.8
5.10
5.11
5.12
5.13
5.15
5.16
5.17
5.18
5.20
5.21
5.22
5.24
5.25
5.26
5.27
5.28
5.29
5.30
5.31
5.33
5.34
5.35
5.36
6.1
6.2
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.19
6.21
6.22
6.23
6.25
6.26
6.27
6.28
6.30
6.32
6.33
6.34
6.35
6.36
6.37
6.38
6.39
6.40
6.43
6.50
6.53
6.56
6.57
6.58
6.59
6.60
6.62
6.67
6.68
6.71
6.73
7.1
7.2
7.3
7.4
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.22
7.28
7.29
7.30
7.31
7.32
7.33
7.34
7.35
7.36
7.37
7.38
7.39
7.40
7.41
7.42
7.44
7.45
7.46
7.47
7.48
7.49
7.50
7.51
7.52
7.53
7.54
7.55
7.56
7.57
7.58
7.59
7.60
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
8.21
8.22
8.24
8.25
8.26
8.27
8.28
8.29
8.30
8.31
8.32
8.33
8.34
8.35
8.36
8.38
8.39
8.40
8.41
8.42
8.43
8.44
8.45
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
9.20
9.21
9.22
9.23
9.24
9.25
9.26
9.27
9.28
9.29
9.30
9.31
9.32
9.33
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.15
10.16
10.17
10.18
10.20
10.21
10.23
10.25
10.26
10.27
10.36
10.38
10.43
10.49
10.53
10.54
10.55
10.56
10.58
10.59
10.67
10.69
11.1
11.2
11.3
11.4
11.5
11.9
11.10
11.11
11.12
11.14
11.15
11.16
11.17
11.18
11.19
11.20
11.21
11.22
11.23
11.24
11.25
11.26
11.27
11.28
11.29
11.30
11.31
11.32
11.33
11.34
11.35
11.36
11.37
11.38
11.39
11.40
11.41
11.42
11.44
11.45
11.46
11.47
11.48
11.49
11.50
11.51
11.52
11.53
11.54
11.55
11.56
11.57
11.59
11.60
11.62
11.63
11.64
11.65
11.66
11.67
11.68
11.69
11.70
11.71
11.72
11.73
11.74
11.75
11.78
12.2
12.3
12.4
12.6
12.7
12.8
12.9
12.10
12.11
12.12
12.13
12.14
12.16
12.17
12.18
12.19
12.20
12.21
12.22
12.24
12.25
12.26
12.28
12.29
12.30
12.31
12.32
12.33
12.34
12.36
12.37
12.38
12.39
12.40
12.41
12.43
12.45
12.46
12.47
12.48
12.49
12.50
12.52
12.53
12.54
12.55
12.57
12.58
12.59
12.60
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
13.17
13.19
14.1
14.2
14.3
14.4
14.5
14.8
14.9
14.10
14.13
14.15
14.16
14.17
14.18
14.21
14.22
14.25
14.27
14.28
14.29
14.30
14.31
14.32
14.35
14.36
14.37
14.38
14.41
14.42
14.43
14.44
14.45
14.47
14.48
14.50
14.51
14.52
15.1
15.2
15.3
15.4
15.5
15.7
15.8
15.9
15.10
15.11
15.12
15.13
15.14
15.15
15.16
15.17
15.18
15.21
15.25
15.26
15.27
15.35
15.36
15.37
15.38
15.39
15.40
15.43
15.44
15.47
15.51
15.52
15.53
15.55
15.56
15.65
15.66
16.1
16.3
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.15
16.16
16.17
16.18
16.20
16.21
16.25
16.26
16.27
16.28
16.29
16.30
16.31
16.32
16.33
16.34
16.35
16.36
16.37
16.38
16.39
16.40
16.41
16.42
16.43
16.44
16.45
16.47
16.48
16.55
17.1
17.2
17.3
17.4
17.5
17.6
17.8
17.9
17.10
17.11
17.12
17.13
17.14
17.15
17.16
17.17
17.18
17.19
17.20
17.21
17.22
17.23
17.24
17.25
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.13
18.14
18.15
19.1
19.2
19.3
19.4
19.5
19.13
19.14
19.15
19.16
19.17
19.18
19.19
19.20
19.21
19.22
19.23
19.24
19.25
19.26
19.27
19.28
19.29
19.30
19.31
19.32
19.33
19.34
19.35
19.36
20.1
20.2
20.3
20.4
20.5
20.7
20.8
20.9
20.13
20.14
20.16
20.17
20.18
20.19
20.20
20.21
20.22
20.23
20.24
20.25
20.26
20.29
20.30
21.9
21.11
21.17
21.18
21.20
21.22
21.28
21.33
21.34
21.35
22.2
22.16
22.26
22.27
22.30
22.35
22.36
22.37
23.1
23.2
23.3
23.4
23.5
23.6
23.9
23.10
23.12
23.14
23.16
23.17
23.18
23.20
23.23
23.30
23.40
24.1
24.2
24.3
24.5
24.23
25.6
25.7
25.8
25.10
25.13
25.16
25.18
25.22
25.24
25.33
25.34
25.41
26.1
26.2
26.3
26.4
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
26.17
26.18
26.19
26.20
26.21
26.22
26.23
27.1
27.2
27.5
27.6
27.7
27.8
28.1
28.2
28.3
28.4
28.7
28.10
28.11
28.12
28.13
28.14
28.15
28.21
28.25
28.26
28.32
28.35
28.45
28.46
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8
29.9
29.10
29.11
29.12
29.13
29.14
29.16
29.17
29.18
29.19
29.20
29.21
29.22
29.23
30.1
30.2
30.3
30.4
30.6
30.7
30.8
30.9
30.10
30.11
30.12
30.13
30.14
30.15
30.16
30.17
30.20
30.21
30.22
30.23
30.24
30.25
30.26
30.27
30.28
30.29
30.30
30.31
30.32
30.33
31.1
31.2
31.3
31.4
31.5
31.6
31.7
31.8
31.9
31.10
31.11
31.13
31.14
31.15
31.16
31.17
31.18
31.19
31.20
31.21
31.22
31.23
31.24
31.25
31.27
31.30
32.2
32.3
32.4
32.6
32.7
32.8
32.9
32.10
32.11
32.12
32.13
32.15
32.16
32.17
32.18
32.19
32.21
33.1
33.2
33.3
33.4
33.7
33.11
34.5
34.6
34.7
34.8
34.9
34.10
34.11
34.12
34.13
34.14
34.15
34.16
34.17
34.18
34.19
34.20
34.21
34.22
35.1
35.2
35.3
35.4
35.5
35.6
35.7
35.9
35.10
36.1
36.2
36.3
36.4
36.6
36.7
36.8
36.9
36.10
36.11
36.12
37.2
37.3
37.5
37.6
37.8
37.9
37.10
37.11
38.1
38.2
38.3
38.4
38.5
38.6
38.7
38.8
38.9
38.10
38.11
38.12
38.13
38.14
38.15
38.16
39.7
39.10
40.1
40.2
40.3
40.4
40.5
40.6
40.7
40.12
40.15
40.16
40.23
40.50
41.1
41.2
41.3
41.4
41.5
41.6
41.7
41.8
41.9
41.10
41.11
41.12
41.13
41.14
41.17
42.1
42.2
42.3
42.4
42.5
42.6
42.7
43.1
43.2
43.3
43.4
43.5
43.6
43.7
43.8
43.9
43.10
43.11
43.12
43.13
43.14
43.15
43.16
44.5
44.8
44.16
44.19
44.21
44.27
45.1
45.2
45.3
45.4
45.5
45.6
45.7
45.8
45.9
45.10
45.22
45.23
45.24
45.25
45.27
45.28
45.33
46.1
46.2
46.14
46.15
46.16
46.18
46.21
46.24
46.36
46.40
46.42
46.67
46.70
46.73
46.74
46.76
47.3
47.6
47.32
47.43
47.62
49.3
49.5
49.9
49.10
49.15
49.19
49.25
50.1
50.6
50.13
50.18
50.20
50.36
51.1
51.8
51.19
51.20