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Two square wells have the same length. Well 1 has walls of
Chapter 41, Problem 6(choose chapter or problem)
Two square wells have the same length. Well 1 has walls of finite height, and well 2 has walls of infinite height. Both wells contain identical quantum particles, one in each well. (i) Is the wavelength of the ground-state wave function (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells? (ii) Is the magnitude of the ground-state momentum (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells? (iii) Is the ground-state energy of the particle (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells?
Questions & Answers
QUESTION:
Two square wells have the same length. Well 1 has walls of finite height, and well 2 has walls of infinite height. Both wells contain identical quantum particles, one in each well. (i) Is the wavelength of the ground-state wave function (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells? (ii) Is the magnitude of the ground-state momentum (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells? (iii) Is the ground-state energy of the particle (a) greater for well 1, (b) greater for well 2, or (c) equal for both wells?
ANSWER:Step 1 of 3
Compare the ground state wave functions in Figures 41.4 and 41.7 in the text.
(i) Answer (a).
The ground state wave function extends somewhat outside the walls of the finite well, so the particle’s wavelength is longer.