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Transcendental equation for a semi-infinite potential well

A semi-infinite potential well is given as shown in the figure.

---------- Figure -------------------

(a) Consider the case when (0<E<Vo).Show the quantization of energy is given by the following transcendental equation:

--------Equation --------------------

(b) A particle of energy E> Vo is incident from the right into the potential region. Calculate the coefficient of reflection for the particle.

Please see the attached file for figure and equation.


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Time independent Schrodinger equation.

In region I, particles can not exist. Wave function is zero.

In region II, Potential ...

Solution Summary

Solution is in a 5-page word document. I have shown each and every step in obtaining an expression for the quantized energy states and reflection coefficient of a semi infinite potential well for the cases of E < Vo and E > Vo respectively. I have used the equation editor to type mathematical expressions. Please download this solution to learn the techniques of solving similar problems in your quantum mechanics course. I have provided very detailed solution. Thank you.