An electron is confined in an infinite square well of width nm

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Stationary states and bound states in one dimension

Problem

An electron is confined in an infinite square well of width

a = 0.500

nm, occupying

0 < x < a

, with

V = 0

inside and

V

infinite outside. The energy levels are

E_n = n^2\pi^2\hbar^2/2m_ea^2

with

n = 1, 2, 3, \dots

((a)) Find the ground-state energy

E_1

, in eV. ((b)) Find

E_3

, in eV. ((c)) The electron drops from the

n = 3

level to the

n = 1

level and one photon carries away the energy difference. Find the photon's wavelength, in nm. Use

\hbar^2/2m_e = 0.0381

eV nm

^2

and

hc = 1240

eV nm.