Discussion
The energy \(E\) and degeneracy \(d\) of the second excited state of a three-dimensional, isotropic quantum harmonic oscillator with angular frequency \(\omega\) are
Answer: A
The second excited state has \(E = \frac{7}{2}\hbar\omega\) and \(d = 6\).
For the 3D isotropic oscillator \(E = (n_{x} + n_{y} + n_{z} + \frac{3}{2})\hbar\omega\). The ground state has n = 0, the first excited state n = 1, and the second excited state n = 2, so \(E = \frac{7}{2}\hbar\omega\).
Its degeneracy is the number of ways to write 2 as \(n_{x} + n_{y} + n_{z}\): (2,0,0), (0,2,0), (0,0,2), (1,1,0), (1,0,1), (0,1,1), six in all, matching \((n + 1)(n + 2)/2 = 6\). d = 3 counts only one of the two kinds of combination. \(\frac{5}{2}\hbar\omega\) is the first excited state, whose degeneracy is 3, not the second.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development