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Unformatted text preview: states of a harmonic oscillator? The ground state is n = 0. What energy photon is given off when an electron in
an inﬁnite 1-D square well transitions from the 2nd
excited state to the ground state?
The ground state is n = 1.
While we use n to denote the levels, note that for some
potentials we use n = 0 for the ground state, while for other
potentials we use n = 1 for the ground state. On a test, we
w ill expect you to know n of the ground state.
Monday, April 1, 2013 Example / Worked Problems II
What is the momentum of an electron in the 1st
excited state of an inﬁnite square well potential?
The inﬁnite square well energy levels are En = n2ħ2π2/2mL2. The ﬁrst
excited state is n = 2.
The only way we know how to get the momentum is from the
energy. The kinetic energy in this state is E2 = 4ħ2π2/2mL2 = 2ħ2π2/
mL2. So we expect the magnitude of the momentum is p = (2mE)½ =
2πħ/L = h/L.
But is this the answer to the question? You need to be careful about
how it is asked. If the "expectation value" of the momentum is
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