Consider an harmonic oscillator with spring constant k and massm.
- Find the classical frequency of this oscillator as a function ofthe spring constant and
m.
In quantum mechanics, the spectrum of possible energies for thisoscillator is given by:
En = hf (n + 1/2) where n is a natural number: n = 0, 1, 2, 3, ...,h is Planckâs constant
and f is the frequency.
- Find the ground state energy as a function of the spring constantand the mass.
- What is the di?erence of energy between the second excited stateand the ground
state?
- Assume now that the oscillator carries a unit of charge, what isthe wavelength of
the photon emitted as a function of k and m when the oscillatorgoes from the ?rst
excited state down to the ground state?
- What is the wavelength of the emitted photon of the previousquestion if k = 10eV /°A
2
,
where °A denotes Angstrom and eV: electron volt. Is the emittedphoton in the visible
spectrum of a human eye?
Consider an harmonic oscillator with spring constant k and massm.
- Find the classical frequency of this oscillator as a function ofthe spring constant and
m.
In quantum mechanics, the spectrum of possible energies for thisoscillator is given by:
En = hf (n + 1/2) where n is a natural number: n = 0, 1, 2, 3, ...,h is Planckâs constant
and f is the frequency.
- Find the ground state energy as a function of the spring constantand the mass.
- What is the di?erence of energy between the second excited stateand the ground
state?
- Assume now that the oscillator carries a unit of charge, what isthe wavelength of
the photon emitted as a function of k and m when the oscillatorgoes from the ?rst
excited state down to the ground state?
- What is the wavelength of the emitted photon of the previousquestion if k = 10eV /°A
2
,
where °A denotes Angstrom and eV: electron volt. Is the emittedphoton in the visible
spectrum of a human eye?
