Concept explainers
(a)
The wave function of the reflected wave.
To verify: The ratio of reflected to incident probability density is
Formula Used:
The coefficient of reflected wave is
Calculation:
Now go back to the two conditions of a valid solution and eliminate the coefficient of the reflecred wave, B.
Solve the combined conditions for the coefficient of the decaying wave, C.
Use the coefficient of the decaying wave, C, the wave number of the incident wave, K, and the decay constant of the decaying wave,
Substitute
Now go back to the two conditions of a valid solution and eliminate the coefficient of the reflected wave, B.
Solve the combined conditions for the coefficient of the decaying wave, C.
Use the coefficient of the decaying wave, C, the wave number of the incident wave, K, and the decay constant of the decaying wave,
Substitute
The ratio of the reflected probability density to the incident probability density can be found by diving the magnitude squared of the reflected wave,
Conclusion:
The ratio of reflected probability density to the icidemt prpability density is
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Modern Physics
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