3. Potential Barrier. A quantum particle with energy E> 0 is incident to the potential barrier described by the potential energy function 0; x <-a V(x)= Voi -a≤x≤a, 0; x> a where Vo> 0. Consider the case where E > Vo. (a) Write down the time-independent Schrödinger equation for the three regions. (b) Solve for the wave function (x) in each region. (c) Applying the boundary conditions, what is the resulting system of equations involving the amplitudes? Hint: There are four equations in this system. (d) Solve for the transmission coefficient T-¹
3. Potential Barrier. A quantum particle with energy E> 0 is incident to the potential barrier described by the potential energy function 0; x <-a V(x)= Voi -a≤x≤a, 0; x> a where Vo> 0. Consider the case where E > Vo. (a) Write down the time-independent Schrödinger equation for the three regions. (b) Solve for the wave function (x) in each region. (c) Applying the boundary conditions, what is the resulting system of equations involving the amplitudes? Hint: There are four equations in this system. (d) Solve for the transmission coefficient T-¹
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Transcribed Image Text:Solve the following problems. Write your solutions clearly
and in detail in a short bond paper or yellow paper.
3. Potential Barrier. A quantum particle with energy E> 0 is incident to the potential barrier described
by the potential energy function
x <-a
0;
V(x)= Vo; -a≤x≤a,
0;
(x) = {
x > a
where Vo > 0. Consider the case where E > Vo.
(a) Write down the time-independent Schrödinger equation for the three regions.
(b) Solve for the wave function (x) in each region.
(c) Applying the boundary conditions, what is the resulting system of equations involving the
amplitudes? Hint: There are four equations in this system.
(d) Solve for the transmission coefficient T-¹
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