{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quantum Engi Q and A_Part_11

# Quantum Engi Q and A_Part_11 - 3.6 THE HARMONIC OSCILLATOR...

This preview shows pages 1–2. Sign up to view the full content.

3.6. THE HARMONIC OSCILLATOR 31 3.6.3.1 Solution harmc-a Question: Verify that the sets of quantum numbers shown in the spectrum figure 3.3 do indeed produce the indicated energy levels. Answer: The generic expression for the energy is E n x n y n z = 2 n x + 2 n y + 2 n z + 3 2 ¯ or defining N = n x + n y + n z , E n x n y n z = 2 N + 3 2 ¯ Now for the bottom level, n x = n y = n z = 0, so N = n x + n y + n z = 0, this state has energy 3 2 ¯ . Similarly, in each of the three sets of the second energy level in figure 3.3, the three quantum numbers n x , n y , and n z add up to N = 1, giving this state energy 5 2 ¯ . For the third energy level, the three quantum numbers of each set add up to N = 2, giving energy 7 2 ¯ , and for the fourth set, the quantum numbers in each of the ten sets add up to N = 3 for an energy 9 2 ¯ . 3.6.3.2 Solution harmc-b Question: Verify that there are no sets of quantum numbers missing in the spectrum figure 3.3; the listed ones are the only ones that produce those energy levels. Answer: The generic expression for the energy is E n x n y n z = 2 n x + 2 n y + 2 n z + 3 2 ¯ or defining N = n x + n y + n z , E n x n y n z = 2 N + 3 2 ¯ Now for the bottom level, N = 0, and since the three quantum numbers n x , n y , and n z cannot be negative, the only way that N = n x + n y + n z can be zero is if all three numbers are zero.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

Quantum Engi Q and A_Part_11 - 3.6 THE HARMONIC OSCILLATOR...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online