Chapter 12: Q4CP (page 480)

Verify that this equation gives the correct number of ways to arrange 0, 1, 2, 3, or 4 quanta among 3 one-dimensional oscillators, given in earlier tables (1, 3, 6, 10, 15).

Q₁
Q₂
#ways1
#ways2
#ways1
#ways2
0
4
1
15
15
1

3

3

10
30
2
2

6

6

36
3

1

10

3

30
4

0

15

1

15


Q₁	Q₂	#ways1	#ways2	#ways1 #ways2
0	4	1	15	15
1	3	3	10	30
2	2	6	6	36
3	1	10	3	30
4	0	15	1	15

Short Answer

Expert verified

The equation gives the correct number of ways to arrange4quanta among 3 one-dimensional oscillators.

Step by step solution

Identification of given data

The given number to arrange is 0,1,2,3,4 quanta.

Concept of permutation

A sequential or linear arrangement of its members, or if the set is already sorted, a reordering of its pieces. An act or procedure of altering the overall sequential order of a predetermined set is referred to as a "permutation."

Determination of the number of ways to arrange quanta in one-dimensional oscillators

The number of ways microstates can be evaluated using

$Ω = \frac{(q + N - 1)!}{q! (N - 1)!}$

Substitute values in the above equation,

$Ω = \frac{(4 + 3 - 1)!}{4! (3 - 1)!} Ω = \frac{6!}{4! 2!} Ω = 15$

Thus, the result is the same in the equation and tabular form.

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Verify that this equation gives the correct number of ways to arrange 0, 1, 2, 3, or 4 quanta among 3 one-dimensional oscillators, given in earlier tables (1, 3, 6, 10, 15).

Q₁
Q₂
#ways1
#ways2
#ways1
#ways2
0
4
1
15
15
1

3

3

10
30
2
2

6

6

36
3

1

10

3

30
4

0

15

1

15

Short Answer

Step by step solution

Identification of given data

Concept of permutation

Determination of the number of ways to arrange quanta in one-dimensional oscillators

One App. One Place for Learning.

Most popular questions from this chapter

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Verify that this equation gives the correct number of ways to arrange 0, 1, 2, 3, or 4 quanta among 3 one-dimensional oscillators, given in earlier tables (1, 3, 6, 10, 15). Q1 Q2 #ways1#ways2 #ways1 #ways2 0 4 115151 3 3 1030 22 6 6 363 1 10 3 304 0 15 1 15

Short Answer

Step by step solution

Identification of given data

Concept of permutation

Determination of the number of ways to arrange quanta in one-dimensional oscillators

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Medical Physics

Astrophysics

Engineering Physics

Particle Model of Matter

Linear Momentum

Study anywhere. Anytime. Across all devices.

Verify that this equation gives the correct number of ways to arrange 0, 1, 2, 3, or 4 quanta among 3 one-dimensional oscillators, given in earlier tables (1, 3, 6, 10, 15).

Q₁
Q₂
#ways1
#ways2
#ways1
#ways2
0
4
1
15
15
1

3

3

10
30
2
2

6

6

36
3

1

10

3

30
4

0

15

1

15