Consider a particle of mass m moving in 1-dimension under a piecewise-constant po- tential. In region I, that corresponds to x <0 the potential energy is Vi(x) = V, > 0. In region II, that corresponds to x > 0 the potential energy is V1(x) = 0. The particle is shot from r = -∞ in the positive direction with energy E > Vo > 0. See the figure %3D %3| in the next page for a representation of V(x) as a function of x. Also shown in the graph (green dashed line) is the energy E of the particle. (a) Which of the following functions corresponds to the wavefunction 1(x) in region I? (al) Aekiæ + Be-ikiæ (а2) Аеҹӕ + Ве-кӕ (а3) Ае*та ; (а4) Ве-куӕ

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(63) Ceiku-
(64) De-KI1¤
(c) What are the boundary conditions that you have to impose on the wavefunction
for this problem?
Vex)
E
Vo
Transcribed Image Text:(63) Ceiku- (64) De-KI1¤ (c) What are the boundary conditions that you have to impose on the wavefunction for this problem? Vex) E Vo
Consider a particle of mass m moving in 1-dimension under a piecewise-constant po-
tential. In region I, that corresponds to x < 0 the potential energy is V(x) = Vo > 0.
In region II, that corresponds to x > 0 the potential energy is V1(x) = 0. The particle
is shot from = -∞ in the positive direction with energy E > Vo > 0. See the figure
in the next page for a representation of V(x) as a function of x. Also shown in the
graph (green dashed line)
the energy E of the particle.
(a) Which of the following functions corresponds to the wavefunction 1(x) in region
I?
(a1) Aeikiæ + Be-iki¤
; (а2) Ае\1 + Bе-кӕ
(a3) Aeikræ
(а4) Ве- кта
(b) Which of the following functions corresponds to the wavefunction 1(x) in region
II?
(b1) Сеkп* + De-ikr
(62) C'e*I1* + De-*1¤
Transcribed Image Text:Consider a particle of mass m moving in 1-dimension under a piecewise-constant po- tential. In region I, that corresponds to x < 0 the potential energy is V(x) = Vo > 0. In region II, that corresponds to x > 0 the potential energy is V1(x) = 0. The particle is shot from = -∞ in the positive direction with energy E > Vo > 0. See the figure in the next page for a representation of V(x) as a function of x. Also shown in the graph (green dashed line) the energy E of the particle. (a) Which of the following functions corresponds to the wavefunction 1(x) in region I? (a1) Aeikiæ + Be-iki¤ ; (а2) Ае\1 + Bе-кӕ (a3) Aeikræ (а4) Ве- кта (b) Which of the following functions corresponds to the wavefunction 1(x) in region II? (b1) Сеkп* + De-ikr (62) C'e*I1* + De-*1¤
Expert Solution
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Given:-

            The time independent in Schrodinger equation is given by:

                              -h22md2ψdx2+Vxψx = Eψx 

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