The Quantum Harmonic Oscillator
6.2 The Quantum Harmonic Oscillator
Learning Objectives
- Describe the model of the quantum harmonic oscillator
- Identify differences between the classical and quantum models of the harmonic oscillator
- Explain physical situations where the classical and the quantum models coincide
Practice!
| Practice 6.2.1 |
|---|
| A quantum mechanical system initially in its ground level absorbs a photon and ends up in the first excited state. The system then absorbs a second photon and ends up in the second excited state. For which of the following systems does the second photon have a longer wavelength than the first one? |
| A. harmonic oscillator |
| B. hydrogen atom |
| C. particle in a box |
Discuss!
Treated as a harmonic oscillator, the carbon monoxide (CO) molecule oscillates with natural (angular) frequency ω0 = 6.5 x 1013 rad/s. If a transition is made between the 3rd excited state (n = 3) and the ground state, what is the wavelength of the radiation emitted?
What region of the electromagnetic spectrum does this correspond to?
The wave function 
is a solution to the simple harmonic oscillator problem.
Find the energy of this state.
At what position, x, are you least likely to find the particle?
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