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Unformatted text preview: PHYSICS 309L, Spring 2010
HOMEWORK 9, due Monday 04/26/10 1. A particle is conﬁned in a cubic box, each side measures 1Angstrom. The mass of the
particle is 10−30 kg . The potential energy inside the box is zero, outside the box it is
inﬁnite. Use the Heisenberg uncertainty principle to ﬁnd the lowest possible momentum
for the particle and calculate the lowest possible energy for this particle in eV.
2. Consider an harmonic oscillator with spring constant k and mass m.
- Find the classical frequency of this oscillator as a function of the spring constant and
In quantum mechanics, the spectrum of possible energies for this oscillator is given by:
En = hf (N +1/2) where n is a natural number: n = 0, 1, 2, 3, ..., h is Planck’s constant
and f is the frequency.
- Find the ground state energy as a function of the spring constant and the mass.
- What is the diﬀerence of energy between the second excited state and the ground
- Assume now that the oscillator carries a unit of charge, what is the wavelength of
the photon emitted as a function of k and m when the oscillator goes from the ﬁrst
excited state down to the ground state?
- What is the wavelength of the emitted photon of the previous question if k = 10eV /˚ ,
where ˚ denotes Angstrom and eV: electron volt. Is the emitted photon in the visible
spectrum of a human eye? ...
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