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Found in: Page 186

### Modern Physics

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

# Consider a particle bound in a infinite well, where the potential inside is not constant but a linearly varying function. Suppose the particle is in a fairly high energy state, so that its wave function stretches across the entire well; that is isn’t caught in the “low spot”. Decide how ,if at all, its wavelength should vary. Then sketch a plausible wave function.

The graph is plotted with energy and potential inside a potential well.

See the step by step solution

## Step 1 : Location of turning points

If potential rises higher than the particles total energy then the particle is stuck in the potential well and it oscillates between the turning points and it cannot escape. Hence the turning points in this condition is located thus the oscillator wave function stretches across the entire well with quantum states with node and antinode.

## Step 2 : Relation with kinetic energy and wavelength

As the kinetic energy varies inversely with wavelength, amplitude becomes larger at the regions where kinetic energy is smaller and the wavelength will be shortened for region where kinetic energy is larger

For high potential inside a well , the particles wave function tunnels through the finite potential barrier and is finally brought to zero.

## Step 3 : Graph

the plausible wavefunction is

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