Question 1 An electron is trapped in a region between two infinitely high energy barriers. In the region between the walls the potential energy of the electron is zero. The normalised wave function of the electron in the region between the walls is ?(?) = ? sin ??, where ? = 0.50 nm−1/2 and ? = 1.18 nm−1 . (a) Calculate the energy of the electron in this state of motion.
Question 1
An electron is trapped in a region between two infinitely high energy barriers. In the region
between the walls the potential energy of the electron is zero. The normalised wave
function of the electron in the region between the walls is ?(?) = ? sin ??, where ? =
0.50 nm−1/2
and ? = 1.18 nm−1
.
(a) Calculate the energy of the electron in this state of motion.
Question 2
In some physical situations, the behaviour of an electron can be approximated as if the
electron were bound to an equilibrium position by a spring force (?(?) = −??, ?(?) =
??
2
2
,
where ? is the spring constant). Suppose such an electron were in the first excited state,
with a wave function ?(?) = ???
−??
2
, where ? is a constant, ? = √??/2ℏ and ?
represents the distance of the electron from its equilibrium position.
(a) Calculate the energy of the electron in terms of ? and its mass ?.
(b) If the electron behaved like a classical oscillating particle, the largest value of ?
would be ??. Show that ?? = √3ℏ. (??)
−1/4
.
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