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Modern Physics
Found in: Page 186
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

Equation gives infinite well energies. Because equation cannot be solved in closed form, there is no similar compact formula for finite well energies. Still many conclusions can be drawn without one. Argue on largely qualitative grounds that if the walls of a finite well are moved close together but not changed in height, then the well must progressively hold fewer bound states. (Make a clear connection between the width of the well and the height of the walls).

Answer:

When the walls of our infinite well are drawn closer together, the wavelengths of standing waves shorten, and the particle is no longer imprisoned in that condition.

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Step by Step Solution

Step 1: Theory of Infinite well energy

The wavelengths of the standing waves get shorter when the walls of our infinite well are pulled closer together, suggesting greater momentum and, in turn, kinetic energy. The kinetic energies of some states will exceed the height of the potential energy walls as the walls become closer together, and the particle will no longer be trapped in that state.

Step 2: Theory for wall energy

When the walls of our infinite well are brought closer together, the wavelengths of the standing waves shorten, implying more momentum and, hence, kinetic energy. As the potential energy barriers move closer together, the kinetic energies of some states will exceed the height of the potential energy walls, and the particle will no longer be imprisoned in that state.

As the walls are brought together the particle will no longer be imprisoned in that state.

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